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