Adjuvant chemotherapy after surgery other than that specified in this protocol is not allowed; luteinizing hormone-releasing hormone (LHRH) agonists and adjuvant bisphosphonate or denosumab use is allowed All patients must be receiving standard of care androgen deprivation treatment (surgical castration versus LHRH agonist or antagonist treatment); subjects receiving LHRH agonist or antagonist must continue treatment throughout the time on this study Previous hormonal therapy, such as LHRH agonists (e.g., leuprolide, goserelin, buserelin, triptorelin) or LHRH antagonist (e.g. degarelix), anti-androgens (e.g., flutamide, bicalutamide, cyproterone acetate), estrogens (e.g., diethylstilbestrol [DES]), or surgical castration (orchiectomy) Prior androgen deprivation (luteinizing hormone-releasing hormone [LHRH] agonist and/or non-steroidal anti-androgen) is allowed if discontinued at least 90 days prior to study enrollment and given for =< 90 days duration\r\n* For example: Patients on prior LHRH analogs (post-prostatectomy), the discontinuation date should be calculated based on the expected duration of the sustained release injection, not simply the injection date of the drug; for instance, if a 22.5 mg sustained release dose of leuprolide acetate is given (3 month duration), then the expected duration of such a dose would be 90 days after the injection date; for a 7.5 mg leuprolide (1 month duration), the discontinuation date would be 30 days after the injection date\r\n* Please note: Finasteride or dutasteride must be stopped before treatment but should not determine eligibility Prior androgen deprivation therapy (luteinizing hormone-releasing hormone [LHRH] agonist and/or non-steroidal anti-androgen) is allowed if discontinued at least 90 days prior to Step 1 registration and given for =< 90 days duration\r\n* For example: patients on prior LHRH analogs (post-prostatectomy), the discontinuation date should be calculated based on the expected duration of the sustained release injection, not simply the injection date of the drug; for instance, if a 22.5 mg sustained release dose of leuprolide acetate is given (3 month duration), then the expected duration of such a dose would be 90 days after the injection date; for a 7.5 mg leuprolide (1 month duration), the discontinuation date would be 30 days after the injection date \r\n* Please note: finasteride or dutasteride must be stopped before treatment starts but prior usage will not affect eligibility Have testosterone < 50 ng/dL; patients must continue primary androgen deprivation with an luteinizing hormone-releasing hormone (LHRH) analogue (agonist or antagonist) if they have not undergone orchiectomy Hormonal-acting agents (including DES, aldosterone, and spironolactone but not including gonadotropin-releasing hormone [GnRH] agonists or antagonists) are forbidden during the trial and must be stopped prior to treatment start; no washout period will be required for any of these agents Must have undergone bilateral orchiectomy (surgical castration) or be willing to continue gonadotropin-releasing hormone (GnRH) analog or antagonist (medical castration) Serum testosterone < 50 ng/dL; patients must continue primary androgen deprivation with a luteinizing-releasing hormone (LHRH) analogue (agonist or antagonist) if they have not undergone orchiectomy On Androgen Deprivation Therapy (ADT) with a Gonadotropin-releasing hormone (GnRH) agonist/antagonist or prior bilateral orchiectomy. All patients will be required to be on ADT throughout the study; Surgically or medically castrated. The testosterone levels do not need to be checked if the patient has undergone surgical castration for >4 months. Patients receiving chemical castration should have testosterone levels checked at baseline and confirmed to be in the castrate levels (<0.5 ng/mL or 1.735 nM). In all cases the luteinizing hormone-releasing hormone (LHRH) antagonist/agonist is to be continued in these patients. Castrate testosterone levels (< 50 ng/dL) achieved by orchiectomy or maintenance on a luteinizing hormone-releasing hormone (LHRH) agonist or antagonist Testosterone < 50 ng/dL; patients must continue primary androgen deprivation with an gonadotrophin releasing hormone (LHRH) analogue if they have not undergone orchiectomy For all Parts except Part F and H: Participants must have either post-menopausal status or pre-menopausal status if continuing or beginning ovarian suppression with a luteinizing hormone-releasing hormone (LHRH) agonist such as goserelin. Have received systemic anti-cancer treatment or radiotherapy less than 2 weeks before the first dose of AG-270. Subjects with castration-resistant prostate cancer may continue therapy with a luteinizing hormone releasing hormone (LHRH) agonist while participating in this study. Continuation of supportive therapy with bisphosphonates or denosumab is also allowed, regardless of the underlying malignancy. Age <60 and amenorrhea for 12 or more months (in the absence of chemotherapy, tamoxifen, toremifen, or ovarian suppression) and follicle-stimulating hormone (FSH) value >40 milli-international units per milliliter (mIU/mL) and an estradiol value <40 picograms per milliliter (pg/mL) (140 picomoles per liter [pmol/L]). Or ii. Premenopausal or perimenopausal concurrently given a luteinizing hormone-releasing hormone (LHRH) agonist starting at least 4 weeks before the start of trial therapy and is planned to continue LHRH during the study. Patients must not be on active luteinizing hormone-releasing hormone (LHRH) agonist/antagonist therapy and must have testosterone level > 50 ng/dL Testosterone =< 50 ng/dL; subjects must continue primary androgen deprivation with an luteinizing hormone-releasing hormone (LHRH) analogue (agonist or antagonist) if they have not undergone orchiectomy intra-uterine hormone-releasing systems (IUSs), Treated with continuous androgen ablative therapy (either surgical castration or luteinizing hormone- releasing hormone [LHRH] agonist/antagonist) No other anticancer-therapy (chemotherapy, immunotherapy, hormonal anti-cancer therapy, radiotherapy [except for palliative local radiotherapy]), biological therapy or other novel agent is to be permitted while the patient is receiving study medication; patients on luteinizing hormone-releasing hormone (LHRH) analogue treatment for more than 6 months are allowed entry into the study and may continue at the discretion of the investigator Ongoing androgen deprivation with gonadotropin-releasing hormone (GnRH) analog or bilateral orchiectomy, with serum testosterone <= 50 ng/dL (<= 1.7 nmol/L) within 28 days before randomization Patients must be castrate-resistant (i.e., developed progression of metastases following surgical castration or during medical androgen ablation therapy). Patients receiving medical castration therapy with gonadotropin-releasing hormone analogues should continue this treatment during this study. Subject has prior use of any hormones, including luteinizing hormone-releasing hormone (LHRH) agonists, ketoconazole, antiandrogens (such as bicalutamide, flutamide, or nilutamide), or 5-alpha-reductase inhibitors Ongoing androgen deprivation therapy with a gonadotropin-releasing hormone (GnRH) analogue or orchiectomy (i.e., surgical or medical castration); patients who have not had an orchiectomy must maintain effective GnRH-analogue therapy for the duration of the trial If no prior orchiectomy has been performed, patients must remain on luteinizing hormone-releasing hormone (LHRH) agonist or antagonist (e.g. degarelix) therapy; patients who are receiving an antiandrogen as part of primary androgen ablation must demonstrate disease progression following discontinuation of the antiandrogen, defined as two consecutive rising PSA values, obtained at least two weeks apart, or documented osseous or soft tissue progression; at least one of the PSA values must be obtained at least four weeks (flutamide) or six weeks (bicalutamide or nilutamide) after discontinuation Patients with prostate cancer can continue to receive treatment with gonadotropin releasing hormone (GnRH) agonists while on study, as long as there is evidence of disease progression on therapy Part B2: Participants must have advanced, recurrent, or metastatic breast cancer that is refractory to aromatase inhibitors (AI) with either disease recurrence or disease progression; must be hormone receptor positive (HR+) and human epidermal growth factor receptor 2 (HER2)-negative; must be of postmenopausal status or beginning ovarian suppression with a luteinizing hormone-releasing hormone (LHRH) agonist Serum testosterone < 50 ng/dL. Subjects must continue primary androgen deprivation with an LHRH analogue (agonist or antagonist) if they have not undergone orchiectomy Patients must have undergone bilateral surgical castration or must continue on gonadotrophin releasing hormone (GnRH) agonists/antagonists for the duration of the study. Concurrent use of gonadotrophin releasing hormone (GnRH) analogue (i.e. medical castration) with testosterone at screening < 50 ng/dL Patients must agree to continuation of androgen deprivation therapy (ADT) with a gonadotropin-releasing hormone analogue/antagonist or bilateral orchiectomy; (patients with a malignancy other than prostate cancer are excluded from this criterion) Patients must agree to continue to continuation of androgen deprivation therapy (ADT) with a gonadotropin-releasing hormone analogue/antagonist or bilateral orchiectomy Prior surgical or chemical castration with serum testosterone <1.7 nmol/L (50 ng/dL). If the method of castration is use of a luteinizing hormone releasing hormone (LHRH) analogue,there must be a plan to maintain effective LHRH analogue treatment for the duration of the trial More than 2 months of prior ADT with gonadotrophin releasing hormone (GnRH) antagonist/agonist at time of consent. Bicalutamide given for =< 2 months at the time of registration as flare prevention is allowed Prior hormone therapy for prostate cancer including orchiectomy, antiandrogens, ketoconazole, or estrogens (5-alpha reductase inhibitors allowed), or luteinizing hormone-releasing hormone (LHRH) agonists/antagonists Initiated 28 (+ 7) days of androgen deprivation therapy (ADT) prior to day 1 of protocol therapy\r\n* Only luteinizing hormone-releasing hormone (LHRH) agonist treatment is considered ADT, bicalutamide or other antiandrogens used alone do not count Ongoing androgen deprivation therapy with a gonadotropin releasing hormone (GnRH) analogue or orchiectomy (i.e., surgical or medical castration) Ongoing androgen deprivation therapy (ADT) with a gonadotropin-releasing hormone (GnRH) analogue or bilateral orchiectomy Patients must agree to continuation of androgen deprivation therapy (ADT) with a gonadotropin-releasing hormone agonist/antagonist or bilateral orchiectomy More than 1 month of prior hormone exposure or hormone exposure within 30 days of enrollment (up to 1 month of prior luteinizing hormone-releasing hormone (LHRH) agonist and/or anti-androgen therapy as neoadjuvant therapy prior to prostatectomy is allowed); prior enzalutamide, apalutamide, ketoconazole, abiraterone, or TAK700 for prostate cancer are prohibited; prior antiandrogen therapy (including but not limited to bicalutamide, flutamide, nilutamide, enzalutamide, and apalutamide) and prior estrogen therapy (including estrogen patch) are not allowed; all investigational agents are prohibited within 30 days of enrollment Men who have had gonadotrophin releasing hormone (LHRH) agonist or antagonist hormone therapy in the prior six months Prior hormone therapy for prostate cancer including orchiectomy, antiandrogens, ketoconazole, or estrogens (5-alpha reductase inhibitors allowed), or LHRH agonists/antagonists (Note: LHRH allowed if begun within 1 month of day 1). Patients undergoing any systemic therapy (except for luteinizing hormone-releasing [LHRH] hormone agonist or antagonist treatment for prostate cancer, and bisphosphonates or receptor activator of nuclear factor [Nf] kappa [RANK] ligand inhibitors for bone strengthening), major surgery or radiotherapy for the treatment of prostate cancer within 2 weeks of study entry. No prior hormonal therapy with the exception of oral 5-alpha-reductase inhibitors (finasteride, dutasteride, etc.); patients who have received prior oral anti-androgen therapies (bicalutamide, flutamide, nilutamide, etc.) must be off treatment for at least 6 weeks prior to enrollment; patients who have received prior luteinizing hormone-releasing hormone (LHRH) agonist or antagonist therapy (leuprolide, goserelin acetate, etc.) are eligible provided serum testosterone is > 50 mg/dl Patients who have had chemotherapy, radiotherapy, immunotherapy or anticancer agents within 4 weeks (6 weeks for nitrosoureas or mitomycin C) of the first dose of study treatment, except hormonal therapy with luteinizing hormone-releasing hormone (LHRH) analogues for medical castration in patients with prostate cancer and breast cancer, which are permitted Last dose of any antineoplastic therapy >= 2 weeks (including chemotherapy, small molecule inhibitors, radiation, and/or other investigational anticancer agents); patients receiving hormone manipulation (e.g. selective estrogen receptor modulators [SERMs], aromatase inhibitors, luteinizing hormone releasing hormone [LHRH] agonist, etc.) for reasons other than treatment of metastatic breast cancer may continue this treatment at the discretion of the investigator Prior hormone therapy for prostate cancer including orchiectomy, antiandrogens, ketoconazole, or estrogens (5-alpha reductase inhibitors allowed), or luteinizing hormone-releasing hormone (LHRH) agonists/antagonists. Bilateral orchiectomy or ongoing androgen deprivation therapy with a gonadotropin-releasing hormone (GnRH) agonist/antagonist (surgical or medical castration). The following ongoing treatments are permitted:\r\n* Hormone-replacement therapy or oral contraceptives\r\n* Hormone therapy for primary prevention of breast cancer Serum testosterone < 50 ng/dL; patients must continue primary anti-androgen therapy (ADT) with a luteinizing hormone-releasing hormone (LHRH) analogue (agonist or antagonist) if they have not undergone orchiectomy Treatment naive, defined as less than 2 months of standard of care ADT (e.g. gonadotrophin releasing hormone [GNRH] agonist or antagonist with or without antiandrogen, including abiraterone) for metastatic hormone-sensitive prostate cancer prior to enrollment (at time of consent) Treated with continuous androgen ablative therapy (either surgical castration or gonadotrophin releasing hormone [LHRH] agonist/antagonist) with documented castrate level of serum testosterone (< 50 ng/dl) Ongoing androgen deprivation therapy (ADT) using an luteinizing hormone-releasing hormone (LHRH) agonist (e.g. leuprolide, goserelin) or antagonist (e.g. degarelix) must continue on therapy unless prior bilateral orchiectomy has been performed; OR screening serum testosterone must be =< 50 ng/dl Patients must have been surgically or medically castrated; if the method of castration was luteinizing hormone-releasing hormone (LHRH) agonists (leuprolide or goserelin) or antagonists (degarelix), then the patient must be willing to continue the use of LHRH agonists or antagonists; serum testosterone must be at castration levels (< 50 ng/dL) within 3 months prior to registration Patients must agree to continue to continuation of androgen deprivation therapy (ADT) with a gonadotropin-releasing hormone agonist/antagonist or bilateral orchiectomy Ongoing androgen deprivation therapy with a luteinizing hormone-releasing hormone (LHRH) \super-agonist\ or antagonist, or bilateral orchiectomy and serum testosterone level < 50 ng/dL (< 0.5 ng/mL, < 1.7 nmol/L) at screening. Patients must have been surgically or medically castrated; if the method of castration was luteinizing hormone-releasing hormone (LHRH) agonists (leuprolide or goserelin) or antagonists (degarelix), then the patient must be willing to continue the use of LHRH agonists or antagonists; serum testosterone must be at castration levels (< 50 ng/dL) within 3 months prior to registration The use of any prior hormones including luteinizing hormone–releasing hormone (LHRH) agonists, LHRH antagonists, antiandrogens such as bicalutamide, flutamide and nilutamide, and/or the use of 5-alpha reductase inhibitors, PCSPES (or PC-x product), megestrol acetate, or estrogen containing nutraceuticals within 6 months of\r\nstudy treatment initiation mCRPC EXPANSION COHORT: Patients must have undergone bilateral surgical castration or must agree to continue on gonadotrophin releasing hormone (GnRH) agonists/antagonists for the duration of the study Concurrent standard long-term anticancer hormonal therapy with drugs including, but not limited to, selective estrogen receptor modulators or Gonadotropin-releasing hormone (GnRH) analogs if started at least six months before the first dose of ARQ 751 is allowed Treatment within 28 days of cycle1 day1: any other systemic therapy for prostate cancer (with the exception of luteinizing hormone-releasing hormone [LHRH] agonists and LHRH antagonists for testosterone suppression, and bisphosphonates and RANK-ligand inhibitors for bone metastases which are allowed); any other investigational product Patients must be off prior chemotherapy, hormonal therapy, or biological therapy for at least 4 weeks or > 3 half-lives whichever comes first; patients with prostate cancer may continue to receive luteinizing hormone–releasing hormone (LHRH) agonist (unless orchiectomy has been performed) Concurrent use of other anticancer agents or treatments, with the following exceptions:\r\n* Ongoing treatment with luteinizing hormone-releasing hormone (LHRH) agonists or antagonists, denosumab (Prolia) or bisphosphonate (eg, zoledronic acid) is allowed; ongoing treatment should be kept at a stable schedule; however, if medically required, a change of dose, compound, or both is allowed Ongoing gonadal androgen deprivation therapy with gonadotropin-releasing hormone (GnRH) analogues, antagonists or orchiectomy; patients who have not had an orchiectomy must be maintained on effective GnRH analogue/antagonist therapy Ongoing gonadal androgen deprivation therapy with gonadotropin-releasing hormone (GnRH) analogues, antagonists or orchiectomy; patients who have not had an orchiectomy must be maintained on effective GnRH analogue/antagonist therapy Prior surgical castration or concurrent use of gonadotropin-releasing hormone (GnRH) analogue (i.e. medical castration) with testosterone at screening < 50 ng/dL Patient deemed eligible for complete androgen blockade, and androgen deprivation therapy by treating physician (this includes consideration of baseline liver function prior to initiation of therapy, if necessary at physician’s discretion); for patients not eligible for anti-testosterone therapy, hormone therapy with gonadotrophin releasing hormone (LHRH) agonist alone will be permitted on case by case by study principal investigator; AS can be any LHRH agonists, LHRG antagonists or anti-androgens that are approved for androgen suppression for the treatment of prostate cancer Patients must have been surgically or medically castrated; if the method of castration was luteinizing hormone-releasing hormone (LHRH) agonists (leuprolide or goserelin), then the patient must be willing to continue the use of LHRH agonists; serum testosterone must be at castrate levels (< 50 ng/dL) at least 14 days prior to registration Hormonal therapy (luteinizing hormone-releasing hormone [LHRH] agonist or oral anti-androgen) exceeding 4 months prior to registration Previous hormonal therapy, such as luteinizing hormone-releasing hormone (LHRH) agonists (e.g., goserelin, leuprolide) or LHRH antagonists (e.g., degarelix), anti-androgens (e.g., flutamide, bicalutamide), estrogens (e.g., diethylstilbestrol [DES]), or surgical castration (orchiectomy) Progressing on continuous androgen ablative therapy (either surgical castration or luteinizing hormone-releasing hormone [LHRH] agonist) For castration-only Cohort C, patients must have developed castrate resistant prostate cancer after progressing on first line hormone therapy with either surgical castration or LHRH agonist or LHRH agonist plus an anti-androgen Previous hormonal therapy, such as luteinizing hormone-releasing hormone (LHRH) agonists (e.g., leuprolide, goserelin, buserelin, triptorelin) or LHRH antagonist (e.g. degarelix), anti-androgens (e.g., flutamide, bicalutamide, cyproterone acetate), estrogens (e.g., diethylstilbestrol [DES]), or surgical castration (orchiectomy) Ongoing androgen deprivation therapy (ADT) using a luteinizing hormone-releasing hormone (LHRH) agonist (e.g. leuprolide, goserelin) or antagonist (e.g. degarelix) must continue on therapy unless prior bilateral orchiectomy has been performed Prior hormonal therapy (luteinizing hormone-releasing hormone [LHRH] agonist/antagonist with or without antiandrogen) up to 8 weeks is permitted Prior hormonal therapy, such as luteinizing hormone-releasing hormone (LHRH) agonists (e.g., goserelin, leuprolide), antiandrogens (e.g., flutamide, bicalutamide), estrogens (e.g., diethylstilbestrol [DES]), or bilateral orchiectomy Androgen suppression therapy within past year; defined as: luteinizing hormone-releasing hormone (LHRH) agonist or antagonist, or androgen blocker, not 5-alpha reductase inhibitor At least 28 days elapsed between last anti-cancer treatment administration and the initiation of study treatment (except for Luteinizing Hormone-releasing Hormone [LHRH] or Gonadotropin-releasing Hormone [GnRH]), or resolution of all previous treatment related toxicities to CTCAE version 4.03 grade of ? 1 (except for chemotherapy induced alopecia and grade 2 peripheral neuropathy or grade 2 urinary frequency which are allowed). Prior major surgery must be at least 12 weeks prior to study entry. Oestrogens, including hormone replacement therapy; No other anticancer-therapy (chemotherapy, immunotherapy, hormonal anti-cancer therapy, radiotherapy [except for palliative local radiotherapy]), biological therapy or other novel agent is to be permitted while the patient is receiving study medication; patients on luteinizing hormone-releasing hormone (LHRH) analogue treatment for more than 6 months are allowed entry into the study and may continue at the discretion of the investigator Ongoing gonadal androgen deprivation therapy with gonadotropin-releasing hormone (GnRH) analogues, antagonists or orchiectomy; patients who have not had an orchiectomy must be maintained on effective GnRH analogue/antagonist therapy Pre/perimenopausal women with a known hypersensitivity to gonadotrophin releasing hormone (gnRH). Surgically or medically castrated, with testosterone levels of < 50 ng/dL; if the patient is medically castrated, continuous dosing with luteinizing hormone-releasing hormone (LHRH) analogue must have been initiated at least 4 weeks prior to randomization and must be continued throughout the study to maintain castrate levels of testosterone including post-treatment follow up period Patients must have been surgically or medically castrated; if the method of castration was luteinizing hormone-releasing hormone (LHRH) agonists (leuprolide or goserelin) or antagonists (degarelix), then the patient must be willing to continue the use of LHRH agonists or antagonists; serum testosterone must be at castration levels (< 50 ng/dL) within 3 months prior to registration Non-pregnant and not nursing; women of childbearing potential must take the pregnancy test and must commit to receive luteinizing hormone-releasing hormone (LHRH) agonist Zoladex (goserelin) for two years starting from the commencement of the study medications Surgically or medically castrated, with testosterone levels of <=50 nanograms per deciliter (ng/dL) (<2.0 nanometer [nM]). If the patient is being treated with luteinizing hormone-releasing hormone (LHRH) agonists/antagonists (patient who have not undergone orchiectomy) this therapy must have been initiated at least 4 weeks prior to Cycle 1 Day 1 and must be continued throughout the study. Received hormonal therapy (apart from luteinizing hormone releasing hormone agonist/antagonist for prostate cancer and hormone replacement therapy) within 2 weeks prior to the first dose of study treatment Received hormonal therapy (apart from luteinizing hormone releasing hormone agonist/antagonist for prostate cancer and hormone replacement therapy) within 2 weeks prior to the first dose of study treatment TUMOR BIOPSY SEQUENCING: Patients with bone metastases or hypercalcemia on intravenous bisphosphonate treatment, denosumab, or similar agents areare eligible to participate and may continue this treatment; patients with prostate cancer may continue luteinizing hormone-releasing hormone (LHRH) agonists or antagonists Prior history of up to 8 weeks of androgen deprivation therapy defined as luteinizing-hormone releasing hormone (LHRH) or other medical castration therapy prior to registration is acceptable; this will be in addition to the 6 months of ADT on study Prior orchiectomy or must be on ongoing luteinizing hormone-releasing hormone (LHRH) agonist or antagonist (e.g., degarelix) therapy Men who have received any hormonal manipulation (antiandrogens; luteinizing hormone-releasing hormone [LHRH] agonist; 5-alpha-reductase inhibitors) within the previous 6 months Patients with prostate cancer can continue to receive treatment with gonadotropin-releasing hormone (GnRH) agonists while on study, as long as there is evidence of disease progression on therapy Prior treatment with an anti-androgen, luteinizing hormone-releasing hormone (LHRH) agonist, or a combination of the two There are two patient populations eligible for the study: those who have not started any therapy with LHRH agonist or antagonist (or orchiectomy) (Early Induction Group) and those who have already started therapy with LHRH agonist or antagonist (or orchiectomy) within the 30 days prior to registration (Late Induction Group); patients must be registered within 30 days of first injection of the LHRH agonist or antagonist (or orchiectomy) In the late induction group, patients must have had no more than 30 days of prior castration (medical or surgical) for metastatic prostate cancer prior to registration; the start date of medical castration is considered the day the patient first received an injection of a LHRH agonist/antagonist (or orchiectomy), not an oral antiandrogen\r\n* If the method of castration was luteinizing hormone releasing hormone (LHRH) agonists (i.e., leuprolide or goserelin), the patient must be willing to continue the use of LHRH agonist and add bicalutamide or TAK-700 (according to randomization) during protocol treatment\r\n* If the patient was on an antiandrogen (e.g. bicalutamide, flutamide), the patient must be willing to switch over to bicalutamide or TAK-700 (according to randomization); there is no limit on how many days a patient may have been on an antiandrogen (e.g. bicalutamide, flutamide) or a five alpha reductase inhibitor (e.g. finasteride or dutasteride) prior to going on study and no washout is required\r\n* If the method of castration was LHRH antagonists (i.e. Degarelix), the patient must be willing to switch to an LHRH agonist during protocol treatment Has ongoing androgen deprivation with serum testosterone <50 ng/dL (<2.0 nM). Treatment with luteinizing hormone-releasing hormone agonists or antagonists must have been initiated ?4 weeks prior to first dose of study therapy and must be continued throughout the study negative serum pregnancy test at baseline (within 14 days prior to randomization) and agree to use medically approved precautions to prevent pregnancy during the study and for 12 weeks following the last dose of abemaciclib id menopause induced by gonadotropin-releasing hormone (GnRH) agonist or radiation Castration resistant disease defined as ongoing androgen deprivation therapy with gonadotropin-releasing hormone (GnRH) analogue or bilateral orchiectomy and serum testosterone level ? 1.73 nmol/l (50 ng/dL) at screening visit. Individuals who have not had a bilateral orchiectomy must have a plan to maintain effective GnRH-analogue therapy for the duration of the trial. Anti-tumor therapy (chemotherapy, antibody therapy, molecular targeted therapy) within 21 days or 5 half-lives, whichever is longer, of study drug dosing (6 weeks for nitrosoureas, mitomycin C, or molecular agents with t1/2 > 10 days); concurrent use of an luteinizing hormone releasing hormone (LHRH) agonist is permitted for all individuals and ongoing enzalutamide is required in Group 3. Age < 55 years and surgical menopause with bilateral oophorectomy a. Note: Ovarian radiation or treatment with a luteinizing hormone-releasing hormone (LH-RH) agonist (goserelin acetate or leuprolide acetate) is not permitted for induction of ovarian suppression at the time of screening. Long term use (>6 months prior to screening) is permitted Once randomized at day 1, subject must maintain ADT with an LHRH agonist or antagonist during study treatment or have a history of bilateral orchiectomy (i.e., medical or surgical castration). Ongoing androgen deprivation therapy with a gonadotropin-releasing hormone (GnRH) agonist/antagonist or prior bilateral orchiectomy (medical or surgical castration); Prior therapy for prostate cancer (exceptions: luteinizing hormone-releasing hormone [LHRH] agonist or antagonist may have been initiated within 30 days prior to enrollment; bicalutamide may have been given within 60 days of enrollment as long as it has been stopped at least 7 days before enrollment and total duration was no longer than 30 days; previous alpha-reductase inhibitor use allowed IF patient has not been taking for at least 30 days prior to abiraterone acetate initiation, OR if alpha reductase inhibitor was not used as a primary treatment of prostate cancer and the PSA on alpha-reductase inhibitor remains within eligibility when doubled Ongoing androgen deprivation therapy (ADT) with a Gonadotropin-releasing hormone (GnRH) analogue or a surgical/medical castration with testosterone level of ?1.73nmol/L (50ng/dL) Pre-/peri-menopausal women can be enrolled if amenable to be treated with the luteinizing-hormone releasing hormone (LHRH) agonist, goserelin. Individuals must have commenced treatment with goserelin or an alternative LHRH agonist at least 4 weeks prior to first dose of study drug. If individuals have received an alternative LHRH agonist prior to study entry, they must switch to goserelin on or before Cycle 1 Day 1 (C1D1) for the duration of the study EARLY INDUCTION GROUP: Subjects who have started androgen deprivation therapy (luteinizing hormone-releasing hormone (LHRH) agonist or antagonist therapy with or without an anti-androgen agent) a maximum of 28 days before registration and who otherwise meet all the eligibility criteria. LATE INDUCTION GROUP: Subjects who have NOT started any androgen deprivation therapy (luteinizing hormone-releasing hormone (LHRH) agonist or antagonist therapy with or without an antiandrogen agent). Patients with prior surgical or chemical castration with a serum testosterone of <50 ng/mL. If the method of castration is luteinizing hormone releasing level hormone (LHRH) agonists, the patient must be willing to continue the use of LHRH agonists during protocol treatment. Have a history of uncontrolled pituitary hormone diseases that currently require varying doses of supplemental hormonal administration (thyroid hormones, adrenocorticotropic hormone [ACTH], growth hormone) or other endocrine disorders requiring varying doses of hormone administration with the exception of diabetes and osteoporosis Castrate level of serum testosterone (< 50 ng/mL) achieved by prior hormonal therapy consisting of either a) orchiectomy or b) luteinizing hormone-releasing hormone (LHRH) agonists with or without an anti-androgen Prior hormonal therapy, such as LHRH agonists (e.g., goserelin, leuprolide), antiandrogens (e.g., flutamide, bicalutamide), estrogens (e.g., diethylstilbestrol [DES]), or bilateral orchiectomy Androgen deprivation therapy (if applicable) initiated > 3 months prior to registration; patients who have undergone bilateral orchiectomy will be eligible if they meet all other criteria; NOTE: patients with a history of locally recurrent hormone refractory cancer are eligible for this study, not patients with metastatic hormone refractory prostate cancer Ongoing androgen depletion therapy with a Gonadotropin Releasing Hormone analog or inhibitor, or orchiectomy (surgical or medical castration) Previous hormonal therapy such as luteinizing hormone releasing hormone (LHRH) agonists (e.g. goserelin, leuprolide), anti-androgens (e.g. flutamide, bicalutamide), estrogens (e.g. diethylstilbestrol [DES]), or surgical castration (orchiectomy) Throughout the study, ongoing androgen deprivation therapy with a luteinizing hormone-releasing hormone (LHRH) analogue or prior bilateral orchiectomy (medical or surgical castration); Patients must have undergone orchiectomy, or have been on LHRH agonists or antagonists, for at least 3 months prior to study entry. Patients on LHRH agonists/antagonists must remain on these agents for the duration of the study. Subjects who are currently taking or have received hormones (eg, estrogen or progesterone) within 7 days the first dose of study drug. Note: Luteinizing hormone-releasing hormone (LHRH) analogs are permissible. Have had either surgical castration OR be on luteinizing hormone-releasing hormone (LHRH) agonist or antagonist therapy with serum testosterone < 50 ng/dl AND agree to stay on LHRH agonist or antagonist therapy during the study Prior hormone therapy for prostate cancer including orchiectomy, antiandrogens (including first-generation antiandrogens, enzalutamide, ARN-509 and others), cytochrome P450, family 17 (CYP17) inhibitors (including abiraterone, TAK-700, galeterone, ketoconazole, and others), estrogens, luteinizing hormone-releasing hormone (LHRH) agonist/antagonists; topical ketoconazole and other topical antifungal agents are allowed; prior therapy with 5alpha-reductase inhibitors is allowed; LHRH therapy allowed if begun within 4 weeks of day 1\r\n* Prior androgens are allowed if the patient had a testosterone within the normal range prior to starting androgens and the androgens have been stopped for at least 7 days The subject must have castration-resistant prostate cancer (CRPC) with castrate levels of serum testosterone less than 50 ng/dL; Note: subjects must maintain a castrate state; if they have not had an orchiectomy must continue to receive luteinizing-hormone-releasing hormone (LHRH) or gonadotropin-releasing hormone (GnRH) agonists unless intolerant Castration resistant prostatic adenocarcinoma; subjects must have castrated levels of serum testosterone (< 50 ng/dL) achieved by orchiectomy or luteinizing hormone-releasing hormone (LHRH) agonist or antagonist therapy Have postmenopausal status due to either surgical/natural menopause or ovarian suppression (initiated at least 28 days prior to Day 1 of Cycle 1) with a gonadotropin-releasing hormone (GnRH) agonist such as goserelin Ongoing androgen depletion therapy with a gonadotropin releasing hormone (GnRH) analogue or inhibitor, or orchiectomy (i.e., surgical or medical castration); for patients who have not had an orchiectomy, there must be a plan to maintain effective GnRH-analogue therapy for the duration of the trial All patients who have not initiated hormone therapy (early induction patients) must have elevated PSA >= 4 ng/ml within 28 days prior to registration; for late induction registrations, PSA must be >= 4 ng/ml prior to start of androgen deprivation therapy; either antiandrogen or LHRH analogue or gonadotropin-releasing hormone (GNRH) antagonist; if patients are on antiandrogen, this will need to be discontinued for at least 7 days prior to registration Patients who are being treated with a GNRH antagonist should be willing to switch to a LHRH analogue after registration Patients with rising PSA must have had either 1) prior definitive therapy including surgery or radiation therapy (hormone-naïve, defined as hormone-naïve patients and patients who received hormone therapy in the past who currently have total testosterone greater than 50 ng/dL), or 2) hormone suppressive therapy as documented by surgical castration or a serum testosterone value less than 50 ng/dL (hormone-independent). Patients must have completed these therapies for at least 6 months but no longer than 20 years prior to enrollment Currently on androgen ablation hormone therapy (a luteinizing hormone-releasing hormone [LHRH] agonist/antagonist or orchiectomy) with testosterone level < 50 ng/dL) Patients must have a one week washout period from prior hormonal therapy (e.g. testosterone, estrogen, progestin, gonadotropin-releasing hormone antagonist) Participants without orchiectomy must be maintained on luteinizing-hormone-releasing hormone (LHRH) agonist/antagonist therapy Bilateral orchiectomy or maintenance on androgen ablation therapy with luteinizing-hormone-releasing hormone (LHRH) agonist or antagonist, or polyestradiol phosphate COHORT A: More than 5 months of prior hormonal therapy (e.g., gonadotropin hormone releasing analogs, megestrol acetate, or Casodex); there is no washout period required for gonadotropin hormone releasing (GnRH) analogs; a two week washout period is required for megestrol or anti-androgen Subject has ongoing androgen deprivation therapy with a Gonadotropin-releasing hormone (GnRH) analogue (agonist or antagonist) or bilateral orchiectomy (i.e., surgical or medical castration). Surgically or medically castrated, with testosterone levels of < 50 ng/dL (< 2.0 nM); if the patient is being treated with luteinizing hormone-releasing hormone (LHRH) agonists (patient who have not undergone orchiectomy), this therapy must have been initiated at least 4 weeks prior to cycle 1 day 1 and must be continued throughout the study Patients must not have previously received hormonal therapy (luteinizing hormone-releasing hormone [LHRH] agonist, antiandrogen, or both), with the exception of neoadjuvant or adjuvant hormones given in conjunction with prostatectomy; in such cases, hormone therapy must have been administered for =< 6 months, discontinued >= 6 months ago, and serum testosterone must be >= 150 ng/dL Participants without orchiectomy must be maintained on luteinizing hormone-releasing hormone (LHRH) agonist/antagonist therapy Ongoing androgen-deprivation therapy (ADT) using a luteinizing hormone-releasing hormone (LHRH) agonist (e.g. leuprolide, goserelin) or antagonist (e.g. degarelix) must continue on therapy unless prior bilateral orchiectomy has been performed; screening serum testosterone must be =< 50 ng/dl Prior androgen deprivation with luteinizing hormone-releasing hormone (LHRH) is permitted provided that testosterone levels prior to study entry have recovered to normal limits per reference laboratory Patients must agree to continue to continuation of androgen deprivation therapy (ADT) with a gonadotropin-releasing hormone analogue/antagonist or bilateral orchiectomy Castrate levels of testosterone (testosterone < 50 ng/dL) on androgen deprivation therapy (ADT). Patients who have not undergone orchiectomy will continue gonadotropin releasing hormone (GnRH) agonist or antagonist therapy. Ongoing androgen deprivation therapy with a gonadotropin-releasing hormone (GnRH) analogue or bilateral orchiectomy (i.e., surgical or medical castration) Newly diagnosed androgen-dependent prostate cancer; patients already on androgen-dependent therapy (ADT) are eligible as long as the time from initiation of luteinizing-hormone-releasing hormone (LHRH) analog or antagonist is not greater than 3 months Have testosterone < 50 ng/dL; patients must continue primary androgen-deprivation with a luteinizing hormone-releasing hormone (LHRH) analogue if they have not undergone orchiectomy Patients on bisphosphonates for any cancer or on hormone therapy for prostate cancer will not need to discontinue this therapy to be eligible; however, patients with prostate cancer will need to have metastatic prostate cancer that has progressed despite hormonal therapy; castrate testosterone levels occur within hours after castration and within 2 to 3 weeks of a luteinizing hormone-releasing hormone agonist; the current standard is to continue androgen suppression despite progressive disease For cohorts 1, 2, and 4 only: current or prior hormonal therapy (e.g., gonadotropin hormone releasing analogs, megestrol acetate, or antiandrogens) are exclusionary A PSA of > 0.2 ng/ml after 6-18 months of androgen suppression therapy, which may consist of luteinizing hormone-releasing hormone (LHRH) agonist or antagonist alone or the combination of an LHRH agonist or antagonist plus an antiandrogen, such as bicalutamide; androgen suppression therapy will continue without interruption Patients currently being treated with a gonadotropin-releasing hormone (GnRH agonist), bicalutamide or with bisphosphonates may continue treatment while on clinical trial PU-H71 as long as the treatment has been initiated before the study start; GnRH agonist must have been well tolerated for at least three months I 04. Effective castration (serum testosterone levels ?0.50 ng/mL) by orchiectomy and/or luteinizing hormone-releasing hormone (LHRH) agonists or antagonist with or without anti-androgens. Serum testosterone levels < 50 ng/dL (unless surgically castrate); patients must continue androgen deprivation with an luteinizing hormone releasing hormone (LHRH) agonist if they have not undergone orchiectomy Is willing to maintain androgen deprivation therapy with a gonadotropin-releasing hormone (GnRH) agonist/antagonist or has had a bilateral orchiectomy; The exclusion criteria apply only to patients starting new treatment with enzalutamide after receiving placebo as randomized treatment. Each patient must not meet any of the following criteria: Ongoing androgen depletion therapy with a Gonadotropin Releasing Hormone (GnRH) analogue or inhibitor, or orchiectomy (i.e., surgical or medical castration) Ongoing monthly gonadotrophin releasing hormone (GNRH) agonist is required in pre-menopausal women or male participants for at least 4 weeks prior to study entry Ongoing androgen depletion therapy with a gonadotropin-releasing hormone (GnRH) analog or inhibitor, or orchiectomy (i.e., surgical or medical castration). Note: patients who have not undergone orchiectomy must continue GnRH analog therapy for the duration of this protocol. No therapy modulating testosterone levels (such as luteinizing-hormone releasing-hormone agonists/antagonists and antiandrogens) is permitted within 12 months prior to enrollment; agents such as 5alpha-reductase inhibitors, ketoconazole, megestrol acetate, systemic steroids (replacement doses of steroids are allowed), PC-SPES, Saw Palmetto are not permitted at any time during the period that the PSA values are being collected >90 days post hormone therapy usages, subjects who have or are currently undergoing hormone therapy (GnRH agonist/antagonist) must discontinue hormone therapy and go through a 90 day washout period prior to consideration for study participation, and must remain off hormone therapy throughout the duration of the follow-up period (5 years); No prior treatment for prostate cancer including prior surgery (excluding TURP), pelvic lymph node dissection, radiation therapy, or chemotherapy; patients may have received up to 4 months of androgen deprivation therapy (luteinizing hormone releasing hormone [LHRH] agonists, antiandrogens, or both) prior to being enrolled on the study Ongoing androgen deprivation therapy with a luteinizing hormone-releasing hormone (LHRH) agonist or antagonist, or bilateral orchiectomy and serum testosterone level < 50 ng/dL (< 0.5 ng/mL, < 1.7 nmol/L) at screening Castrate testosterone levels at screening with continued Luteinizing hormone-releasing hormone (LHRH) therapy CRPC participants must maintain ongoing androgen deprivation therapy with a gonadotropin releasing hormone (GnRH) analogue, antagonist or orchiectomy providing serum testosterone is <50 ng/dL (<1.7 nmol/L) Ongoing androgen deprivation therapy with an gonadotropin releasing hormone (GnRH) analogue or prior bilateral orchiectomy (medical or surgical castration). For patients who have not had bilateral orchiectomy, there must be a plan to maintain effective GnRH-analogue for the duration of the trial. Ongoing gonadal androgen deprivation therapy with LHRH analogues or orchiectomy. Patients, who have not had an orchiectomy, must be maintained on standard dosing of LHRH analogue therapy at appropriate frequency for the duration of the study Has not received systemic therapy for prostate cancer (i.e. luteinizing-hormone-releasing hormone [LHRH] agonist/antagonist therapy) Subjects who are currently on gonadotropin-releasing hormone (GnRH) agonists or antagonist therapy must continue androgen suppression Postmenopausal; use of luteinizing hormone-releasing hormone (LHRH) agonist permitted Concurrent use of other anticancer agents or treatments except luteinizing hormone-releasing hormone (LHRH) antagonists, LHRH agonists, zoledronic acid and other bone targeting agents =< 2 regimens of cytotoxic chemotherapy prior to study entry; retinoids, vitamin D analogues, peroxisome proliferator-activated receptor (PPAR) gamma agonists or antagonists, antiandrogens, progestational agents, estrogens, prostate cancer (PC)-SPES, luteinizing hormone-releasing hormone (LHRH)-analogues, vaccines, cytokines will not be considered \cytotoxics\; patients who have previously received ketoconazole + glucocorticoids will be eligible for this trial Progressive metastatic prostate cancer (positive bone scan or measurable disease) despite castrate levels of testosterone (either from orchiectomy or luteinizing hormone-releasing hormone [LHRH] agonist therapy) Hormonal anticancer therapies except for LHRH antagonists or LHRH agonists in hormone-refractory prostate cancer Patients must have castrate levels of testosterone (< 50 ng/dL) on gonadotropin-releasing hormone (GnRH) analogues or have had prior orchiectomy; GnRH analogues must be continued while on study Patients with prostate cancer must continue to receive gonadotropin-releasing hormone (GnRH) agonist therapy (unless orchiectomy has been done); if a patient has refused GnRH therapy, they may be enrolled on a dose level for which the safety has already been determined Patients must have had evidence of disease progression while receiving primary androgen suppression therapy by orchiectomy or other primary hormonal therapy and abiraterone (specifically, patients can have received multiple prior additional androgen axis targeting agents including enzalutamide, and prior chemotherapy, but must have had progression while receiving abiraterone either currently or in the past)\r\n* Patients currently on abiraterone may continue with the start of the study drug(s)\r\n* Patients may continue luteinizing hormone-releasing hormone (LHRH) agonist therapy (e.g., leuprolide or goserelin) or LHRH antagonist (e.g. aberelix); patients who have not undergone bilateral orchiectomy may continue LHRH therapy while on protocol Prior androgen deprivation therapy (ADT) with luteinizing hormone-releasing hormone (LHRH) agonist and/or antagonist allowed for either (neo)adjuvant treatment with local therapy or for biochemical relapse Last effective dose of LHRH agonist/antagonist “expired” > 3 months prior to study entry; for example, a patient receiving LHRH agonist injection every 3 months would be eligible provided their last injection was > 6 months prior to day 1 of protocol therapy; a patient receiving LHRH agonist injections every 4 months will be eligible provided last injection was > 7 months prior to day 1 of protocol therapy Hormonal therapy with gonadotropin-releasing hormone (GnRH) agonists, GnRH antagonists or high dose bicalutamide within 1 month of enrollment unless serum testosterone is within normal limits Ongoing androgen deprivation therapy with a gonadotropin releasing hormone (GnRH) analogue or orchiectomy (i.e., surgical or medical castration) Any type of systemic anticancer agent (including investigational) within 3 weeks of first dose of study treatment, or within 5 half-lives of the agent whichever is shorter; subjects on luteinizing-hormone-releasing hormone (LHRH) or gonadotropin-releasing hormone (GnRH) agonists may be maintained on these agents Men with metastatic prostate cancer that require castration therapy with either using an luteinizing hormone-releasing hormone (LHRH) analogue or surgical castration are eligible; complete androgen blockade using anti-androgen therapy prior to castration or up to approximately 4-6 weeks following castration therapy is permitted to prevent disease flare; thereafter anti-androgen therapy may continue or be discontinued based on treating physicians preference; or\r\n* Any men with prostate cancer who are candidates for castration therapy despite no evidence of definite metastatic disease including patient with biochemical failure or rising PSA are also permitted to enter study provided castration therapy is planned for a minimum of a year; patients with biochemical failure prior to enrollment should have also have already received appropriate salvage therapy; men with prostate cancer who have already started castration therapy are also permitted to enter study provided castration therapy was initiated within one month of study entry; or\r\n* Men with prostate cancer previously treated with castration therapy for management of localized prostate cancer in the adjuvant setting or in combination with radiation therapy are permitted to enter study provided they currently have known metastatic disease and have non-castrate testosterone levels (testosterone > 50 ng/dL) Surgical castration or ongoing use of gonadotropin-releasing hormone agonists with confirmed castrate levels of testosterone Have discontinued previous treatments for cancer and recovered from the acute effects of therapy (for example, at least 42 days for mitomycin-C or nitrosoureas, 28 days for other chemotherapy and biologics. At the discretion of the investigator, hormone refractory prostate cancer patients who are stable on gonadotropin-releasing hormone (GnRH) agonist therapy and breast cancer patients who are stable on antiestrogen therapy (for example, an aromatase inhibitor) may continue treatment Ongoing androgen deprivation therapy with a gonadotropin releasing hormone (GnRH) analogue or inhibitor, or orchiectomy (i.e., surgical or medical castration); Prior hormone therapy for prostate cancer including orchiectomy, antiandrogens, ketoconazole, or estrogens (5-alpha reductase inhibitors allowed), or luteinizing hormone-releasing hormone (LHRH) agonists/antagonists Ongoing systemic therapy (other than a luteinizing hormone-releasing hormone agonists [LHRH] agonist/antagonist) for prostate cancer including, but not limited to:\r\n* CYP-17 inhibitors (e.g. ketoconazole, abiraterone)\r\n* Antiandrogens (e.g. bicalutamide, nilutamide)\r\n* Second generation antiandrogens (e.g. ARN-509)\r\n* Immunotherapy (e.g. sipuleucel-T)\r\n* Chemotherapy (e.g. docetaxel, cabazitaxel)\r\n* Radiopharmaceutical therapy (e.g. radium-223, strontium-89, samarium- 153) NOTE: use of luteinizing hormone-releasing hormone (LHRH) agonists (e.g., leuprolide or goserelin) is not allowed Use of any of the following medications within the past 6 months: testosterone, dehydroepiandrosterone (DHEA), estrogens, gonadotropin-releasing hormone (GnRH) analogs, antiandrogens, spironolactone, ketoconazole, recombinant human growth hormone (rhGH), megestrol acetate, prednisone 20 mg daily or equivalent doses of other glucocorticoids for more than two weeks Planned treatment with castration therapy (gonadotropin-releasing hormone [GnRH] agonist/antagonist) for >= 8 months Prior hormone therapy for prostate cancer including orchiectomy, antiandrogens (including first-generation antiandrogens, enzalutamide, apalutamide and others), CYP17 inhibitors (including abiraterone, TAK-700, galeterone, ketoconazole, and others), estrogens, luteinizing hormone releasing hormone (LHRH) agonist/antagonists; prior therapy with 5-alpha-reductase inhibitors is allowed; LHRH therapy allowed if begun within 4 weeks of day 1; up to 30 days of bicalutamide is allowed if it is stopped two weeks prior to day 1 Men > 18 diagnosed with prostate cancer for which antiandrogen therapy (ADT) (castration therapy) is being prescribed for at least 16 weeks; castration may be achieved surgically or using gonadotrophin releasing hormone (LHRH) agonists (i.e. leuprolide, goserelin, etc.) or LHRH antagonists (i.e. degarelix) Hormone replacement therapy in the last three months Post-menopausal status, as defined by institutional guidelines; concurrent gonadotropin-releasing hormone (GnRH) agonist therapy is allowed Medical indication for androgen deprivation therapy (ADT) via luteinizing hormone-releasing hormone (LHRH) analog +/- oral anti-androgen Be on androgen deprivation therapy (ADT) with a gonadotropin-releasing hormone (GnRH) agonist/antagonist or prior bilateral orchiectomy; all patients will be required to be on ADT during the study period PROSTATE CANCER: Patients who are initiating any chemotherapy (examples are docetaxel, cabazitaxel, etc.) and/or hormone directed treatment for prostate cancer; examples of hormone directed therapy include gonadotropin releasing hormone (GnRH) agonist or antagonists (such as leuprolide, goserelin, triptorelin, histrelin and degarelix), androgen receptor blockers (such as bicalutamide or enzalutamide), or androgen biosynthesis inhibitors (such as abiraterone) Second malignancies are allowed as long as the disease does not require active treatment with concomitant systemic cytotoxic chemotherapy, investigational or biologic therapy (e.g., anti-cytotoxic T-lymphocyte-associated protein 4 [CTLA4] or human epidermal growth factor receptor 2 [HER2] monoclonal antibodies); hormone-related therapies (e.g., gonadotrophin releasing hormone (LHRH) agonists, tamoxifen, etc.) are allowed Diagnosed with prostate cancer\r\n* Treatment with ADT (gonadotropin-releasing hormone [GnRH] agonist/antagonist with or without anti-androgen) for prostate cancer\r\n* Receiving ADT for a minimum of 12 weeks before enrollment into the study\r\n* Planned ADT for the duration of the 12-week study period Receiving or planning to receive androgen deprivation therapy (ADT) with luteinizing hormone-releasing hormone (LHRH) agonist or antagonist First dose of LHRH agonist or antagonist no more than 6 months prior to date of study content Men ? 30 years of age with non-metastatic prostate cancer, having undergone bilateral orchiectomy or initiated androgen deprivation therapy (ADT) with gonadotropin-releasing hormone (GnRH) agonists and is expected to continue on ADT for at least 12 months Arm 1 patients may not have received any prior luteinizing-hormone-releasing hormone (LHRH) agonists/antagonists, antiandrogens, or chemotherapy for their prostate cancer; treatment with 5-alpha reductase inhibitors (finasteride, dutasteride) are allowed Have been previously diagnosed with a malignant solid tumor, completed their required surgical, and/or chemotherapy and/or radiation curative intent therapy at least three months prior to enrollment, and have an anticipated treatment-free life span of 12 months or longer; chemoprophylaxis with tamoxifen or aromatase inhibitors for breast cancer in women and anti-luteinizing hormone releasing hormone (LHRH) therapy for prostate cancer in men will be permitted Use of endocrine therapy (selective estrogen receptor modulator, aromatase inhibitor, gonadotrophin releasing hormone [GnRH] agonist) within 6 months of start of study Taking luteinizing hormone-releasing hormone (LHRH) agonists, androgen receptor blocking agents, finasteride, or has undergone bilateral orchiectomy Documentation of menopausal status: postmenopausal subjects or pre-menopausal subjects with ovarian radiation or concomitant therapy with a luteinizing hormone-releasing hormone (LH-RH) agonist/antagonist are eligible. Have testosterone < 50 ng/dL; patients must continue primary androgen deprivation with an luteinizing hormone-releasing hormone (LHRH)/GnRH analogue (agonist or antagonist) if they have not undergone orchiectomy Currently on therapy aimed at lowering testosterone levels (includes gonadotropin-releasing hormone [GnRH] agonist/antagonist, prior bilateral orchiectomy, oral anti-androgens, or 5-alpha reductase inhibitors); testosterone replacement is allowed but treatment should be stable during the entire study Treatment with chemotherapy, hormone therapy, or other investigational therapy within 3 weeks of first study doses; patients with non-adenocarcinoma of the prostate who may be on luteinizing hormone-releasing hormone agonist/antagonist therapy may continue use Use of aromatase inhibitors, gonadotropin-releasing hormone (GNRH)-agonists i.e. Lupron, Zoladex within the last 6 months Hormone replacement therapy within the last 6 months Note: Ovarian radiation or treatment with a luteinizing hormone-releasing hormone (LH-RH) agonist (goserelin acetate or leuprolide acetate) is not permitted for induction of ovarian suppression Patients must have castrate levels of testosterone (< 50 ng/dL) on luteinizing hormone-releasing hormone (LHRH) analogue or have had prior bilateral orchiectomy, with evidence of castration-resistant disease by Prostate Cancer Working Group 2 (PCWG2) criteria Primary or recurrent castration resistant prostate carcinoma with skeletal and/or nodal involvement not currently undergoing systemic chemotherapy who are about to commence therapy with docetaxel/prednisone; (note that systemic hormonal targeted therapy including luteinizing hormone-releasing hormone [LHRH] agonists [Lupron or Trelstar], other anti-androgens, and/or abiraterone or enzalutamide may be in use) Men who have received any hormonal manipulation (antiandrogens; luteinizing hormone releasing hormone [LHRH] agonist; 5-alpha-reductase inhibitors) within the previous 12 months The subject has biopsy-proven adenocarcinoma of the prostate with intermediate to high risk disease by University of California, San Francisco (UCSF) Cancer of the Prostate Risk Assessment (CAPRA) scoring and possesses a Gleason 4 component to the tumor; subjects will be enrolled either prior to radical prostatectomy (N=5) or prior to initiation of androgen deprivation therapy (luteinizing hormone-releasing hormone [LHRH] agonist +/- antiandrogen) followed by definitive radiation therapy as their primary treatment for prostate cancer (N=5) For part 2 of the study: plans to initiate castrating therapy (with a gonadotropin-releasing hormone [GnRH] antagonist, GnRH agonist, or orchiectomy); an antiandrogen may be started after initial imaging but cannot be used prior to baseline imaging; an antiandrogen is allowed but not required Ongoing treatment with any systemic therapy intended for the treatment of prostate cancer (e.g., antiandrogen or LHRH agonist or antagonist) Patient must have surgical resection followed by systemic adjuvant therapy with an aromatase inhibitor (AIs) as part of planned treatment; any approved AI at standard clinical dosing may be used; in pre-menopausal patients, ovarian suppression with a gonadotropin-releasing hormone (GnRH) agonist will be started prior to initiation of the AI on a separate clinical trial in parallel with the imaging study Premenopausal women will be considered eligible for study participation if they are receiving medical ovarian suppression with luteinizing hormone-releasing hormone (LHRH) agonists with documented estradiol blood levels in their respective postmenopausal ranges. Hormonal therapy (luteinizing hormone-releasing hormone [LHRH] agonist or oral anti-androgen) exceeding 4 months prior to registration Patients may or may not have been treated previously with a nonsteroidal antiandrogen, such as flutamide, bicalutamide or nilutamide; for patients previously treated with an antiandrogen, they must be off treatment for at least 4 weeks (for flutamide) or 6 weeks (for bicalutamide or nilutamide) prior to registration and must have shown PSA progression after discontinuing the anti-androgen Prior pharmacologic androgen ablation for prostate cancer is allowed only if the onset of androgen ablation (both LHRH agonist and oral anti-androgen) is =< 45 days prior to the date of registration Patients on long term (> 6 months) anti-androgen therapy (e.g., flutamide, bicalutamide, nilutamide) will need to be off anti-androgen for 4 weeks (wash out period) and show evidence of disease progression off the anti-androgen; patients that have been on an anti-androgen 6 months or less will need to discontinue anti-androgen therapy prior to treatment start (no wash out period required) Preceding line of treatment included response to anti-androgen, progression documented after withdrawal of the anti-androgen. Receipt of >1 line of therapy that includes a second generation androgen inhibitor for treatment of mCRPC Prior exposure to enzalutamide, ARN-509, or other investigational androgen receptor (AR)-directed therapy Patients may not have received enzalutamide or ARN-509 (another androgen receptor antagonist) in the past Patients treated with first generation anti-androgen as most recent systemic therapy (bicalutamide, nilutamide) must have at least 4 weeks elapsed from treatment discontinuation to start of protocol therapy with evidence of disease progression by Prostate Cancer Working Group 2 (PCWG2) criteria following discontinuation of prior anti-androgen Previous androgen suppression therapy is allowed if it was completed at least 3 months prior to initiation of study treatment Subjects on long term (>= 6 months) first generation anti-androgen therapy (e.g. flutamide, bicalutamide, nilutamide) will need to discontinue anti-androgen therapy for 4 weeks prior to registration (wash out period) and show evidence of disease progression off the anti-androgen; subjects that have been on a first generation anti-androgen 6 months or less will need to discontinue therapy prior to registration (no wash out period required) Subjects on second generation anti-androgen therapy (enzalutamide) or androgen bio-synthesis inhibitor (abiraterone acetate) will need to discontinue therapy 2 weeks prior to registration (wash out period) More than one prior line of therapy with a second generation anti-androgen (enzalutamide, ARN-509, etc.) or androgen bio-synthesis inhibitor (abiraterone acetate, etc.); subject may have had one second generation anti-androgen or androgen bio-synthesis inhibitor but not both sequentially; subjects that have received combination therapy with second generation anti-androgen plus an androgen bio-synthesis inhibitor would be eligible (e.g., enzalutamide plus abiraterone acetate as one line of therapy on a clinical trial) Subjects must not have received any previous androgen deprivation therapy (LHRH agonist or LHRH antagonist) or cytotoxic therapy for prostate cancer in the metastatic setting\r\n* Exceptions\r\n** Patients may have received no more than 30 days of anti-androgen (e.g. bicalutamide) in the metastatic setting prior to the start of study treatment. Prior androgen deprivation therapy and/or first generation anti-androgen (e.g. bicalutamide, nilutamide, flutamide) for biochemically recurrent prostate cancer. Prior ADT and/or first generation anti-androgen in the (neo)adjuvant and/or salvage setting before, during, and/or following radiation or surgery is allowed provided last effective dose of ADT and/or first-generation anti-androgen is > 9 months prior to date of randomization and total duration of prior therapy is ? 36 months. No prior treatment with enzalutamide, ARN-509, ODM-201, galeterone or other investigational androgen receptor (AR) targeted treatment is allowed Prior treatment with enzalutamide or other potent androgen-receptor blockers, approved or experimental (e.g., ARN-509, ODM-201, or galeterone) A minimum of 4 weeks elapsed off of anti-androgen therapy prior to enrollment for flutamide and 6 weeks for bicalutamide and nilutamide without evidence of an anti-androgen withdrawal response; patients who NEVER HAD A PSA decline with the most recent anti-androgen therapy or in whom the response to the most recent anti-androgen was for < 3 months require only a 2 week washout period prior to first dose of study drug Previous treatment with an agent that blocks adrenal androgen synthesis (e.g. abiraterone acetate, TAK-700, TOK-001, ketoconazole) or second generation androgen receptor (AR) antagonists (e.g., BMS 641988, ARN-509,TOK-001) Prior anti-androgen therapy Previous androgen suppression therapy for prostate cancer. Prior androgen suppression therapy for prostate cancer for more than 6 months Expansion Phase: Patients must have progressed while receiving an androgen-directed therapy, as follows: Received prior 2nd generation anti-androgen and require urgent disease response or stabilization Previously treated with enzalutamide or experimental therapies directed against androgen receptor (ie, apalutamide). At least 1 line of androgen receptor (AR)-targeted therapy (for example {e.g Candidates for ADT and docetaxel. Started ADT with or without first generation anti androgen, but no longer than 12 weeks before randomization Treatment with androgen receptor antagonists (bicalutamide, flutamide, nilutamide), 5-alpha reductase inhibitors (finasteride, dutasteride), estrogens, chemotherapy, or biologic therapy within 4 weeks of enrollment (day 1 visit) Prior oral anti-androgen (e.g. bicalutamide, nilutamide, enzalutamide, apalutamide), or androgen synthesis inhibitor (e.g. abiraterone, orteronel) in the past 6 months; 5-alpha reductase inhibitor therapy (e.g. finasteride, dutasteride) is allowed, as long as subject has been stable on medication for past 6 months Subjects who received combined androgen blockade as their first-line hormonal therapy with an antiandrogen must have shown PSA progression after discontinuing the antiandrogen for >= 6 weeks prior to study treatment; no washout is needed after abiraterone or enzalutamide are discontinued; first generation antiandrogens such as bicalutamide must be withdrawn if given as first-line therapy Hormonal therapy (e.g., androgen receptor [AR] antagonists, 5 alpha reductase inhibitors, estrogens) Prior exposure to enzalutamide, androgen receptor antagonist ARN-509 (ARN-509) or other investigational AR-directed therapy in the setting of mCRPC A minimum of 2 weeks elapsed off of antiandrogen therapy prior to registration (i.e. flutamide, nilutamide, and bicalutamide) without evidence of an anti-androgen withdrawal response; an anti-androgen withdrawal response is a PSA level at 2 weeks (or more) off of anti-androgen equal or higher than PSA level when anti-androgen therapy stopped At least 1 line of prior androgen receptor (AR) targeted therapy During the Phase II trial, patient must have been treated with enzalutamide or other second-generation androgen receptor antagonist before enrollment into this trial, and is tested positive for AR-V7 Known androgen receptor (AR) positive breast cancer (AR staining > 10% by immunohistochemistry is considered positive); if the AR status is unknown, the patient can go on study Castrate-resistant disease, defined as follows:\r\n* All patients must have received (and be receiving) standard of care androgen deprivation treatment (surgical castration versus gonadotropin-releasing hormone [GnRH] analogue or antagonist treatment); subjects receiving GnRH analogue or antagonist must continue this treatment throughout the time on this study\r\n* Patients may or may not have been treated previously with a nonsteroidal antiandrogen; for patients previously treated with an antiandrogen, they must be off use of anti-androgen for at least 4 weeks (for flutamide) or 6 weeks (for bicalutamide or nilutamide) prior to registration; moreover, subjects who demonstrate an anti-androgen withdrawal response, defined as a >= 25% decline in PSA within 4-6 week of stopping a nonsteroidal antiandrogen, are not eligible until the PSA rises above the nadir observed after antiandrogen withdrawal\r\n* Patients must have a castrate serum level of testosterone (< 50 ng/dL) within 6 weeks of day 1 Androgen receptor positivity, defined as >= 10% of tumor cell nuclei with immunoreactivity for AR on central review at Vanderbilt Participation in a previous clinical trial of enzalutamide or an investigational agent that inhibits the androgen receptor (ARN-509) or androgen synthesis Patients progressing on LHRH agonist plus an anti-androgen as first line therapy must be off anti-androgen for 4 weeks prior to first treatment with testosterone Prior pharmacologic androgen ablation for prostate cancer is allowed only if the onset of androgen ablation is =< 60 days prior to the date of registration Use of any medications known to affect the serum androgen level Tumor with androgen receptor (AR) expressed >= 4580 copies/ug ribonucleic acid (RNA) Patient has any prior use of anti-androgen therapies. Progression on a prior regimen/line of an androgen synthesis inhibitor for prostate cancer Prior treatment with enzalutamide or any other newer hormonal androgen receptor inhibitor (e.g., apalutamide, ODM-201) Current treatment with anti-androgen is allowed for a maximum of one month to prevent flare response with ADT No ongoing anti-androgen therapy; patients must be off anti-androgen therapy for at least 30 days Prior treatment with: second generation androgen receptor (AR) inhibitors, other investigational AR inhibitors, or CYP17 enzyme inhibitor. Specific eligibility criteria for Part 2 CRPC expansion cohort: Persistent disease with evidence of disease progression following standard therapy(ies) including prior treatment with androgen/androgen receptor directed therapy, including enzalutamide and/or abiraterone Androgen suppression or anti-androgen therapy within the 12 months prior to dosing, for prostate cancer. Anti-androgen receptor antagonist therapy must be bicalutamide. Subjects already started on other anti-androgens must be willing to switch over to bicalutamide. Experienced disease progression after having received 1 prior next generation androgen receptor-targeted therapy for castration-resistant disease Androgen receptor positive (AR+)\r\n* Defined as >= 10% nuclear AR staining by immunohistochemistry (IHC) in either the primary or metastatic lesion\r\n* NOTE: Research testing of AR status is available at City of Hope (COH) Pathology For participants previously treated with first generation anti-androgens (ie, flutamide, nilutamide, or bicalutamide), discontinuation of flutamide or nilutamide therapy must occur greater than (>) 4 weeks (>6 weeks for bicalutamide) prior to start of study drug with no evidence of an anti-androgen withdrawal response (no decline in serum PSA) Started less than 12 weeks prior to randomisation AND Prostate Specific Antigen (PSA) is stable or falling. The 12 weeks starts from whichever of the following occurs earliest: first dose of oral anti- androgen, LHRHA, or surgical castration. Patients who have received TOK-001 (Galeterone®) or any other investigational product directed towards the androgen receptor or androgen biosynthesis. Patients who received a first generation anti-androgen (e.g., bicalutamide, flutamide, nilutamide) as part of their first-line hormonal therapy must have shown progression of disease off the anti-androgen prior to enrollment At least 4 weeks must have elapsed from the use of androgen receptor antagonists (e.g., bicalutamide, flutamide, nilutamide); 5-alpha reductase inhibitors (e.g., dutasteride, finasteride, aminoglutethimide); estrogens; ketoconazole and other anti-cancer pharmacologic therapy prior to enrollment At least 6 weeks must have elapsed from the use of bicalutamide if used as part of an initial combined androgen blockage therapy for more than 6 months or if used as second line hormonal therapy and associated with a PSA response of at least 3 months duration Patients who are receiving an anti-androgen as part of their first-line hormonal therapy must have shown progression of disease off the anti-androgen prior to enrollment At least 4 weeks must have elapsed from the use of androgen receptor antagonists (i.e., flutamide, nilutamide, bicalutamide, enzalutamide); 5-alpha (a) reductase inhibitors (i.e., finasteride, aminoglutethimide); abiraterone acetate; estrogens; nitrosoureas, mitomycin C, isotype therapy, ketoconazole, chemotherapy and other anti-cancer pharmacologic therapy prior to beginning protocol therapy Prior use, or participation in a clinical trial, of an investigational agent that blocks androgen synthesis (e.g., abiraterone acetate, TAK-700, TAK-683, TAK-448) or agents that block the androgen receptor (e.g., ARN-509) Subjects who received combined androgen blockade with an anti-androgen must have shown PSA(prostate specific antigen) progression after discontinuing the anti-androgen prior to enrollment. Prior participation in a clinical trial of an investigational agent that inhibits the androgen receptor or androgen synthesis (unless the treatment was placebo) Previous anti-androgen therapy and progression after withdrawal; patients who received combined androgen blockade with an anti-androgen must have shown PSA progression after discontinuing the anti-androgen prior to enrollment (>= 4 weeks since last flutamide, >= 6 weeks since last bicalutamide or nilutamide) No treatment with any of the following for prostate cancer within 4 weeks prior to enrollment:\r\n* Hormonal therapy (e.g., androgen receptor [AR] antagonists, 5 alpha reductase inhibitors, estrogens); Note: treatment with bicalutamide and nilutamide within 4 weeks prior to enrollment is not allowed; treatment with flutamide within 4 weeks prior to enrollment is not allowed; treatment with all other gonadotropin-releasing hormone (GnRH) analogues or antagonists is allowed\r\n* Chemotherapy\r\n* Biologic therapy\r\n* Investigational therapy\r\n* Immunotherapy No prior anti-androgen therapy (bicalutamide, flutamide or nilutamide) is permitted Patients who have received androgen ablative therapy for less than 8 weeks immediately prior to initiation of study drug are eligible provided they had only PSA evidence of progression (as defined above) with no visible metastases by CT-scan and bone scan (within 6 weeks) prior to starting androgen ablation Demonstration of progression while on androgen blockade Castrate-resistant disease, defined as follows:\r\n* All patients must have received standard of care androgen deprivation treatment before trial entry (surgical castration versus gonadotropin-releasing hormone [GnRH] analogue or antagonist treatment), and subjects receiving GnRH analogue or antagonist must continue this treatment throughout the time on this study\r\n* Patients may have been treated previously with a nonsteroidal antiandrogen, with evidence of disease progression subsequently; subjects must be off use of anti-androgen for at least 4 weeks (for flutamide) or 6 weeks (for bicalutamide or nilutamide) prior to registration\r\n** Subjects who demonstrate an anti-androgen withdrawal response, defined as a >= 25% decline in PSA within 4-6 week of stopping a nonsteroidal antiandrogen are not eligible until the PSA rises above the nadir observed after antiandrogen withdrawal\r\n* Castration levels of testosterone (< 50 ng/dL) within 2 weeks of registration If a patient enters the trial on androgen suppression therapy (AST) that consists of both an LHRH agonist and an oral antiandrogen, both agents should be continued throughout the study; if an antiandrogen is stopped prior to study entry, it should be stopped 4 weeks before for nilutamide and flutamide and 6 weeks before for bicalutamide to ensure that a withdrawal phenomenon does not interfere with interpretation of efficacy results For patients who have been on anti-androgen therapy and had evidence of response to the addition of an anti-androgen (i.e., PSA reduction), patients must have discontinued anti-androgen therapy for at least six weeks (4 weeks for flutamide) without current evidence of an anti-androgen withdrawal response For patients previously treated with first generation anti-androgens (i.e., flutamide, nilutamide, or bicalutamide), discontinuation of flutamide or nilutamide therapy must occur >4 weeks (>6 weeks for bicalutamide) prior to start of study drug with no evidence of an anti-androgen withdrawal response (i.e., no decline in serum PSA). Prior treatment with investigative androgen receptor (AR) agents Subjects must have discontinued additional hormonal (eg bicalutamide, abiraterone, estrogen) therapy prior to the first dose of cabozantinib; no anti-androgen withdrawal period is required Androgen receptor expression testing confirms that the patient’s tumor is AR (+); AR is considered positive if >= 1% of cell nuclei are immunoreactive using the Dako antibody (clone androgen receptor antibody [AR441]); receptor testing may be performed on either primary tumor specimen or tissue from a metastatic site; local testing permitted for eligibility but will require confirmation at Memorial Sloan-Kettering Cancer Center (MSKCC) Patients who have received prior anti-androgen therapy Prior investigational new generation potent anti-androgen therapy (such as ARN 509). Prior progression on one or more androgen-receptor/androgen-synthesis inhibitor therapies (e.g. abiraterone, enzalutamide, apalutamide, TAK-700 and/or galeterone) by Prostate Cancer Working Group 2 (PCWG2) criteria. Prior progression on bicalutamide/nilutamide/flutamide/ketoconazole alone is not allowed. Use of a first-generation anti-androgen such as bicalutamide within 6 weeks of study drug dosing, or flutamide within 4 weeks of study dosing Treatment with androgen receptor antagonists (bicalutamide, flutamide, nilutamide), 5-? reductase inhibitors (finasteride, dutasteride), estrogens, chemotherapy, or biologic therapy within 4 weeks of Day 1 visit Prior therapy with other CYP17 inhibitor(s) or investigational agent(s) targeting the androgen receptor for metastatic prostate cancer Concurrent anti-androgen therapy Previous anti-androgen therapy and progression after withdrawal Patient must have evidence of castration resistant prostate cancer as evidenced by a confirmed rising PSA (per Prostate Cancer Working Group 3 [PCWG3] criteria) and a castrate serum testosterone level (i.e. =< 50 mg/dL); if a subject also received an anti-androgen, he must first progress through antiandrogen withdrawal prior to being eligible; the minimum timeframe to document failure of anti-androgen withdrawal will be four weeks Patients, who have experienced disease progression despite initial hormonal therapy, either by orchiectomy or by using a gonadotropin-releasing hormone (GnRH) agonist in combination with an anti-androgen, must first progress through anti-androgen withdrawal prior to being eligible; the minimum timeframe to document failure of anti-androgen withdrawal will be four weeks; patients on second-line (or beyond) hormonal maneuvers, and patients who had no PSA decline on combined androgen blockade as first line therapy, need not progress through anti-androgen withdrawal (AAW) in order to be eligible Previous androgen blockade (e.g. antiandrogens) given for greater than 2 weeks in the last 3 months; anti-androgens used during the initiation of ADT to avoid a flare phenomenon are acceptable for up to 4 weeks Other investigational agents in addition to LHRH agonist/antagonist are allowed (e.g. novel anti-androgens, androgen synthesis inhibitors) Have received prior investigational anti-androgen therapy, including ARN-509 Patients on long term (> 6 months) anti-androgen therapy (e.g. flutamide, bicalutamide, nilutamide) will need to be off anti-androgen for 4 weeks (wash out period) and show evidence of disease progression off the anti-androgen; patients that have been on an anti-androgen 6 months or less will need to discontinue anti-androgen therapy prior to treatment start (no wash out period required) Be planning to begin a course of at least 4 months of ADT; the ADT is defined as: (a) surgical castration; (b) gonadotropin-releasing hormone (GNRH) antagonist alone; (c) GNRH antagonist with oral androgen receptor blockade, and (d) GNRH antagonist, oral androgen receptor blockade, and 5-alpha reductase inhibitors; we will not include men with only oral anti-androgen therapy such as 5-alpha reductase inhibitors alone or oral anti-androgens alone Androgen ablation (hormone treatment) within the last 3 months Physician prescription of androgen receptor antagonist therapy (examples: bicalutamide, flutamide, or enzalutamide) during time of protocol scans Use of any medications known to affect the serum androgen levels or the PSA Ongoing androgen deprivation therapy with a GnRH analogue, GnRH antagonist, or bilateral orchiectomy Androgen deprivation therapy prior to radiation is allowed. However, it is not acceptable if continued during radiation or as adjuvant therapy. standard of care androgen deprivation treatment progressive disease while receiving androgen deprivation therapy Patients with hormone sensitive disease who received prior androgen deprivation therapy as part of primary/salvage local treatment or patients receiving intermittent androgen deprivation therapy will be allowed to participate Patients receiving denosumab or bisphosphonates for any cancer, or undergoing androgen deprivation therapy for prostate cancer, are eligible for this therapy Prior or planned androgen deprivation or bilateral orchiectomy Previous androgen deprivation therapy lasting more than 6 months Any investigational medicinal product or other systemic chemotherapy, or antibody therapy within 4 weeks prior to the first dose of study treatment, or within 8 weeks after immunotherapy, whichever is the most appropriate and as judged by the Investigator. Note: androgen-deprivation therapy is permitted for patients with prostate cancer. Prior androgen deprivation therapy is allowed and may have been initiated up to 6 months prior to the date of the HDR implant; the complete duration of androgen deprivation therapy can range from 4 months to 36 months provided it has been initiated no more than 6 months prior to the date of the HDR implant PSA >= 0.2 prior to start of androgen deprivation treatment At least 3 weeks from previous cytotoxic chemotherapy or radiation therapy and at least 5 half-lives or 6 weeks, whichever is shorter, after targeted or biologic therapy excepting prior treatment with CTLA 4, PD-1, or PD-L1 blocking antibodies for which only a 2 week interval is required. Patients with prostate cancer, unless orchiectomy has been performed in them, may continue to receive androgen deprivation therapy (ADT), anti-androgen therapy or therapy that interferes with androgenic stimulation. Is a candidate for, in the opinion of the investigator, at least 1 year of continuous androgen deprivation therapy for the management of androgen-sensitive advanced prostate cancer with one of the following clinical disease state presentations: Advanced localized disease not suitable for local primary surgical intervention with curative intent (radiotherapy, cryotherapy, or high frequency ultrasound are allowed after 2 months of androgen deprivation therapy); In the investigator's opinion, is likely to require chemotherapy or surgical therapy for symptomatic disease management within 2 months of initiating androgen deprivation therapy; Previously received GnRH analog or other form of androgen deprivation therapy (estrogen or antiandrogen) for > 18 months total duration. If androgen deprivation therapy was received for ? 18 months total duration, then that therapy must have been completed at least 3 months prior to baseline. If the dosing interval of the depot is longer than 3 months, then the prior androgen deprivation therapy must have been completed at least as long as the dosing interval of the depot; Prior androgen deprivation therapy (ADT) in the past 6 months; prior ADT in context of neoadjuvant/adjuvant primary; prior ADT for biochemical recurrence is allowed, as long as no ADT has been administered in past 6 months and testosterone has recovered (> 150 ng/dl); the total duration of prior ADT should not exceed 24 months Willing to undergo the following therapy: (1st) systemic chemo-hormonal therapy with up to 6-months (around 24 weeks) of neoadjuvant androgen deprivation and up to 6 cycles of chemotherapy, (2nd) definitive local tumor control with adjuvant radiation therapy, and (3rd) consolidative stereotactic radiation to oligometastatic lesions; additionally, must be willing to be treated with a full two years of androgen deprivation Castration resistant disease with confirmed testosterone level ?50 ng/ml under prior androgen deprivation therapy (ADT) Patients must maintain ongoing androgen deprivation therapy with a GnRH analogue, antagonist, or bilateral orchiectomy (i.e., surgical or medical castration) Prior docetaxel as first line therapy in addition to androgen deprivation is allowed Prior androgen deprivation or chemotherapy is allowed if discontinued at least 30 days prior to enrollment Has recovered from all therapy-related toxicity to =< grade 2 (except alopecia, anemia and any signs or symptoms of androgen deprivation therapy) at the time of registration Patients on androgen deprivation therapy (ADT) are allowed Willing to undergo the following therapy: (1st) Systemic chemo-hormonal therapy with up to 6-months (~24 weeks) of neoadjuvant androgen deprivation and up to 6 cycles of chemotherapy, (2nd) definitive local tumor control with prostatectomy +/- adjuvant radiation therapy, and (3rd) consolidative stereotactic radiation to oligometastatic lesions; additionally, must be willing to be treated with a full year of androgen deprivation Prior or second primary malignancies within the last two years (except carcinoma in situ of the cervix, non-metastatic prostate cancer, or basal cell or squamous cell carcinoma of the skin which were treated with local resection only; prior adjuvant androgen deprivation therapy in the case of prostate cancer is permitted, but current adjuvant androgen deprivation therapy is not) No androgen deprivation therapy (ADT) can be prescribed prior to or during radiation therapy The use of androgen deprivation therapy (ADT) prior to registration or during radiation Prior treatment for CaP by surgery, irradiation, local ablative (e.g. cryosurgery or high intensity focused ultrasound) or androgen deprivation therapy. Patients may not be receiving other investigational agents or be receiving concurrent anticancer therapy other than standard androgen deprivation therapy Up to a total of 1 year of androgen deprivation allowed Use of hormonal therapy or androgen deprivation therapy, including enzalutamide, except in the following setting: Patients can be on androgen deprivation therapy Patient must currently be on androgen deprivation or anti-androgen therapy with castrate levels of testosterone (< 50 ng/dl)\r\n* Medical castration should continue until disease progression Radiographic progression at study entry while on androgen deprivation therapy (or after bilateral orchiectomy). A prior course of hormone therapy (androgen deprivation) of greater than 3 months duration Indication to initiate androgen deprivation therapy (ADT) Standard of care medical management of current prostate cancer disease status by the patient’s local oncologist, e.g. androgen deprivation therapy is allowed Prior use of androgen deprivation including enzalutamide Subjects must not have had prior androgen deprivation therapy in the past 6 months History of androgen deprivation therapy within the past 6 months Willingness to be treated with radiation therapy and androgen deprivation therapy Patients must have had prior treatment with bilateral orchiectomy or androgen\n deprivation therapy with an LHRH-blocker with evidence of treatment failure All patients must have a histologically or cytologically proven diagnosis of adenocarcinoma of the prostate; all patients must have metastatic disease as evidenced by soft tissue and/or bony metastases prior to initiation of androgen deprivation therapy Patients who have not yet started androgen deprivation therapy (LHRH agonist/antagonist or orchiectomy) and will not have an LHRH agonist injection until after randomization (early induction group) must have radiographic assessments of all disease including bone scan (or positron emission tomography [PET] scan) within 42 days prior to registration; patients who have started androgen deprivation therapy (LHRH agonist/antagonist or orchiectomy) prior to registration (late induction group) must have radiographic assessments including bone scan (or PET scan) within 42 days prior to start of androgen deprivation therapy (if scans have not been obtained prior to LHRH agonist/antagonist or orchiectomy they must be done within 42 days prior to registration); all disease must be assessed and documented on the Baseline Tumor Assessment Form; NOTE: Androgen deprivation therapy does not include treatment with anti-androgens such as bicalutamide or flutamide or five alpha reductase inhibitors such as finasteride or dutasteride Patients may have received prior androgen deprivation therapy (ADT) - neoadjuvant and/or adjuvant setting only, but it must not have lasted for more than 36 months (note that this is NOT the same as “late induction” as described in Section 5.1b above); single or combination therapy allowed; at least 6 months must have elapsed since completion of androgen deprivation therapy in the neoadjuvant and/or adjuvant setting, and serum testosterone must be > 50 ng/dL (non-castrate levels) within 28 days prior to registration for early induction patients; Note: serum testosterone assessment is required for eligibility for only those with prior treatment with ADT Disease progression despite Androgen Deprivation Therapy Myocardial infarction or cerebrovascular accident within one year from consultation, or other major vascular risk factor which would prevent a patient from receiving appropriate androgen deprivation therapy Progressive disease on androgen deprivation therapy at enrollment; Androgen deprivation therapy started after prostatectomy and prior to step 1 registration for > 6 weeks (42 days) Any prior androgen-deprivation therapy or finasteride as neoadjuvant or adjuvant therapy or for biochemical recurrence must have been discontinued at least 6 months prior to registration. Patients must have started androgen deprivation therapy (bilateral orchiectomy versus luteinizing hormone-releasing hormone [LHRH] agonist, and with or without androgen antagonist) at least one month (4 weeks) prior to enrollment and no more than six months (24 weeks) prior to enrollment; patients must continue the androgen deprivation therapy throughout the study period, and patients are not permitted to change the type of androgen deprivation therapy (e.g. by adding an androgen antagonist) during the course of investigational therapy Patients must have evidence of response to androgen deprivation as defined by a documented decline in serum PSA values from pre-androgen deprivation treatment baseline and without evidence of PSA progression while on androgen deprivation (defined by Prostate Cancer Working Group 2 [PCWG2] criteria as a 25% increase in serum PSA and an absolute increase of 2 ng/mL over nadir) Have progressive metastatic castration resistant prostate cancer, on androgen deprivation therapy, based on as least one of the following criteria: Patient under medications that can affect PSA for the last 3 months prior to MRgFUS treatment (Androgen Deprivation Treatment; alpha reductase inhibitors) Patients may have received prior androgen deprivation therapy (ADT) in the neoadjuvant, adjuvant and/or salvage setting, but must be off therapy for at least 3 months and have a testosterone level > 150 ng/dl Castration-resistant prostate cancer demonstrated during continuous androgen deprivation therapy (ADT), defined as 3 rises of PSA, at least 1 week apart with the last androgen deprivation therapy (PSA) >= 2 nanogram per milliliters (ng/mL) Patients may either be untreated for their newly diagnosed metastatic disease (preferred as much as possible) or have started androgen deprivation therapy; patients who have started androgen deprivation therapy for the treatment of their newly diagnosed metastatic disease are eligible as long as the duration of treatment is less than or equal to 2 weeks (14 days) prior to registration; the start date of androgen deprivation is considered the day the patient first received an injection of a LHRH agonist/antagonist (or orchiectomy), not the date when an oral antiandrogen started Patients must have a minimum PSA >= 5 ng/mL within 60 days of registration or prior to the initiation of androgen deprivation for patients who have started androgen deprivation therapy Patients who have received androgen deprivation therapy for greater than 14 days (LHRH-agonist or antagonist) for the treatment of their newly diagnosed metastatic disease prior to enrollment are not eligible for this study >= 30 days of antiandrogen therapy monotherapy without androgen deprivation therapy Prior androgen deprivation, chemotherapy, surgery, or radiation for prostate cancer COHORT B: More than 3 cycles of intermittent hormones (for the treatment of biochemical recurrence or castration sensitive metastatic disease), with a cycle defined as a period of consistent androgen deprivation therapy (generally 3-12 months) followed by intentional cessation of androgen deprivation therapy (ADT) without reinitiation of ADT until PSA rises Progressive disease on androgen deprivation therapy Patients must agree to continue androgen deprivation therapy with a GnRH agonist/antagonist throughout the study or have had a prior bilateral orchiectomy Subject must have failed at least one course of androgen deprivation therapy (ADT), i.e., treatment with GnRH analogues. Androgen deprivation therapy based on clinician judgment is permitted on study Patients must maintain ongoing androgen deprivation therapy with a GnRH analogue, antagonist, or bilateral orchiectomy (i.e., surgical or medical castration) Patients must be unresponsive to androgen-deprivation therapy (ADT), as indicated by a rising PSA level above the ADT nadir Patients may have been treated with up to 4 months of androgen deprivation therapy Prior androgen deprivation therapy (ADT) allowed if last dose was greater than (>) 6 months prior to randomization No prior androgen deprivation therapy (ADT) or anti-androgen for biochemical relapse Patients may not be receiving other investigational agents or be receiving concurrent anticancer therapy other than androgen deprivation For cohort 3 only: 1-6 months of androgen deprivation therapy (gonadotropin hormone releasing analogs with or without an anti-androgen) prior to prostatectomy with a castrate testosterone level of < 50 ng/dL within 1 month prior to prostatectomy Prior treatment with an luteinizing hormone-releasing hormone (LHRH) agonist or nonsteroidal antiandrogen, except in the following circumstances: Neoadjuvant/adjuvant androgen deprivation therapy administered with radiation therapy or at the time of prostatectomy is acceptable, provided that there was no evidence of PSA progression while on treatment; in this situation, patients must not have received more than 24 months of androgen deprivation treatment, and must not have been treated within 12 months prior to screening; other treatment with androgen deprivation therapy is prohibited Have been on androgen deprivation therapy for a minimum of 6 months, and continue that therapy or an equivalent therapy to suppress testosterone during this trial Has recovered from all therapy-related toxicity to =< grade 2 (except alopecia, anemia and any signs or symptoms of androgen deprivation therapy) Patients who have had prior treatment for prostate cancer by surgery, irradiation, local ablative (i.e., cryosurgery or high-intensity focused ultrasound), or androgen-deprivation therapy are not eligible Ongoing androgen deprivation therapy with a GnRH analogue or bilateral orchiectomy Progressive disease despite ongoing androgen deprivation therapy. Progressive metastatic (M1) disease on androgen deprivation therapy Serum testosterone level: i) Subjects with no history of androgen deprivation therapy: A single measurement greater than 150 ng/dL or 5.2 nmol/L within 3 months of enrollment ii) Subjects with a history of androgen deprivation therapy (either in adjuvant or biochemical relapse setting): Concurrent use of other investigational agents or other prostate cancer therapies (e.g., androgen deprivation therapy) Prior androgen deprivation therapy for prostate cancer Ongoing androgen deprivation therapy Patients may be enrolled if they have had prior palliative radiation therapy; however, this has to have been commenced within 30 days of starting androgen deprivation Patients diagnosed with localized prostate cancer who are about to receive definitive treatment with either radiation with or without androgen deprivation therapy (ADT) or prostatectomy AND who also have a spouse or been in a committed relationship with their partner for at least 6 months who is willing to participate in the study Prior or current androgen deprivation therapy A history of androgen deprivation therapy; patients receiving hormonal therapy in the adjuvant and/or neoadjuvant setting must have discontinued therapy at least 6 months prior to day 1 of treatment AND have a serum testosterone level >= 50 ng/dL and cannot have received more than 18 months of previous ADT Starting or have started androgen deprivation therapy (oral or injection) for prostate cancer treatment within the last 3 months Prior androgen deprivation therapy allowed, provided there is documented evidence of testosterone recovery to > 150 ng/dL and greater than 12 months duration between last “effective” date of ADT and date of study consent Have a diagnosis of prostate cancer and are scheduled to receive radiotherapy with androgen deprivation therapy Patient had prior treatment for prostate cancer (surgery, radiation, local ablative therapy, anti-androgen therapy or androgen deprivation therapy) ELIGIBILITY FOR THE 2-YEAR EXTENSION: Patient has had prior treatment for prostate cancer (surgery, radiation, local ablative therapy, anti-androgen therapy or androgen deprivation therapy) Have had prior treatment for prostate cancer by surgery, irradiation, local ablative (i.e., cryosurgery or high-intensity focused ultrasound), or androgen-deprivation therapy Patient under medications that can affect PSA for the last 3 months prior to MRgFUS treatment (Androgen Deprivation Treatment; alpha reductase inhibitors) Patients with prior androgen deprivation therapy or any investigational neoadjuvant agent or intervention Cohort B Only: [Enrollment is Complete; No longer recruiting subjects] No prior history of androgen deprivation therapy within the last month; however patients who will receive neoadjuvant and concurrent and adjuvant hormonal therapy will be eligible Androgen deprivation therapy (ADT) within 3 months before 68Ga-PSMA-11 PET/CT. Patients who have received androgen deprivation therapy or prior surgery for prostate cancer Must be treatment naive (not have received neoadjuvant chemotherapy, radiation therapy, hormonal therapy, androgen deprivation therapy, or focal ablation techniques (e.g., high intensity focused ultrasound [HiFu]) SUB-STUDY I: Androgen deprivation therapy for prostate cancer SUB-STUDY II: Androgen deprivation therapy for prostate cancer SUB-STUDY III: Radiation therapy or start of standard of care systemic therapy (chemotherapy, androgen deprivation therapy) within 14 days prior to study PET Subjects receiving androgen deprivation therapy (ADT) Androgen deprivation therapy or other neoadjuvant treatments prior to PET imaging and surgery Not on current androgen deprivation therapy or plan for withdrawal of androgen deprivation therapy Androgen deprivation therapy prior to PET imaging Prior androgen deprivation therapy Current or prior androgen deprivation therapy; a history of use of a 5-alpha reductase inhibitor is allowed, provided it was discontinued at least one month prior to study entry Hormone deprivation therapy Can be on androgen deprivation therapy if dose is stable for >= 1 week Patient can remain on androgen deprivation therapy if on the same regimen prior to documentation of progressive metastatic disease Prior radiation therapy, chemotherapy, or androgen-deprivation therapy within 2 weeks prior to study radiotracer administration (washout is one half-life of the drug or 2 weeks, whichever is longest) Androgen deprivation therapy or chemotherapy prior to PET imaging Men who undergo neoadjuvant treatment with androgen deprivation therapy (ADT) or salvage prostatectomy including those who have had brachytherapy will be excluded Participants should not have had prior curative local treatment for prostate cancer, including no radiotherapy or prostatectomy; a maximum 90 days of systemic androgen deprivation therapy prior to registration is allowed Current or prior androgen deprivation therapy; previous use of a 5-alpha reductase inhibitor is allowed, provided it was discontinued at least one month prior to study entry - No androgen deprivation, anti-androgen therapy, chemotherapy, or investigational systemic therapy prior to CTT1057 PET imaging - Must remain on androgen deprivation therapy for duration of trial if no prior bilateral orchiectomy Androgen deprivation therapy (ADT) in the past 3 months Patients must be eligible for and must be planning to undergo androgen deprivation therapy Prior use of androgen deprivation therapy or radiation therapy Must be willing to continue androgen deprivation therapy while on study, if no prior orchiectomy