Patients must not be planning to receive concomitantly other biologic therapy, hormonal therapy, other chemotherapy, surgery or other anti-cancer therapy except radiation therapy while receiving treatment on this protocol; however, patients receiving extended adjuvant endocrine therapy for an earlier ER positive breast cancer treated with curative intent and without recurrence for at least years may continue with their endocrine therapy Patients who already received neo/adjuvant endocrine therapy are eligible as long as they are enrolled within months of initial histological diagnosis and after completing no more than months of adjuvant endocrine therapy. Patients who previously received endocrine therapy within years prior to diagnosis of the current malignancy. Patients who have had any prior chemotherapy, or endocrine therapy for the treatment of breast cancer or any other cancer Corticosteroid therapy and endocrine replacement therapy (L-thyroxine, testosterone, estrogen, desmopressin acetate [DDAVP]) are permissible; any patient already receiving human growth replacement therapy should discontinue this prior to commencing chemotherapy, and should not restart until years from diagnosis Subjects with endocrine AE of any grade are permitted to enroll if they are stably maintained on appropriate replacement therapy and are asymptomatic. Prior neoadjuvant chemotherapy, endocrine therapy, or biologic therapy for current breast cancer [Period ] Patients must not have received any prior chemotherapy, radiation therapy, or endocrine therapy for their current breast cancer; patients who received tamoxifen or raloxifene or another agent for prevention of breast cancer may be included as long as the patient has discontinued the treatment at least one month prior to baseline study biopsy For Part A (LY + letrozole): Except for ongoing therapy with letrozole, the participant must not have received prior systemic endocrine therapy for metastatic disease. For Part B (LY + anastrozole): Except for ongoing therapy with anastrozole, the participant must not have received prior systemic endocrine therapy for metastatic disease. For Part C (LY + tamoxifen): The participant may have received prior systemic endocrine therapy for metastatic disease and may be receiving ongoing therapy with tamoxifen. For Part D (LY + exemestane): The participant must have received prior systemic endocrine therapy with at least one nonsteroidal aromatase inhibitor (anastrozole, letrozole) for metastatic disease and may be receiving ongoing therapy with exemestane. For Part E (LY + exemestane + everolimus): The participant must have received prior systemic endocrine therapy with at least one nonsteroidal aromatase inhibitor (anastrozole, letrozole) for metastatic disease and may be receiving ongoing therapy with either exemestane or exemestane + everolimus. For Part G (abemaciclib + LY + fulvestrant): The participant may have received prior systemic endocrine therapy with at least one nonsteroidal aromatase inhibitor (anastrozole, letrozole) for metastatic disease. ENDOCRINE RESISTANT COHORT: Pre-registration is not required for patients to be enrolled in the endocrine resistant cohort, as PIKCA mutation status will not be assessed ENDOCRINE RESISTANT AND ADJUVANT COHORT: ECOG performance status of , or ENDOCRINE RESISTANT AND ADJUVANT COHORT: Platelets >= ,/mcL ENDOCRINE RESISTANT COHORT: Ki > % by central testing at Washington University AMP laboratory from a tumor biopsy performed after at least weeks on neoadjuvant endocrine therapy; if Ki is > % by local testing, the Ki slide and H&E slide need to be reviewed by the study pathologist to confirm eligibility (discuss with study chair); for patients external to Washington University, please contact the Washington University coordinator by email so that a screening identification (ID)# can be assigned prior to shipment of the slides\r\n* Note that prior neoadjuvant endocrine therapy could include any endocrine therapy (including aromatase inhibitor, tamoxifen, fulvestrant) alone or in combination, or endocrine therapy in combination with any investigational agent that is not a Cdk / inhibitor\r\n* Patients who had a day Ki > % from the NCI trial are eligible for the endocrine resistant cohort\r\n* Note that enrollment to the endocrine resistant cohort will depend on the funding availability; please contact the study chair before enrolling patients to this cohort ENDOCRINE RESISTANT COHORT: Prior treatment of this cancer including:\r\n* Surgery\r\n* Radiation therapy\r\n* Chemotherapy No washout is required for endocrine therapy; if a patient has been on endocrine therapy within days of study entry, that same endocrine therapy is permitted to be continued during protocol therapy, at the investigators discretion, as is continuation of ovarian suppression in premenopausal women; starting a new endocrine therapy during protocol therapy is not permitted Prior systemic therapy:\r\n* Participant must be at least days from the last dose of prior chemotherapy, endocrine therapy, biological agents (including small molecule targeted therapy) or any investigational drug product with adequate recovery of toxicity to baseline, or grade (with the exception of alopecia and hot flashes) at the time of registration\r\n* There is no limit to the number of prior lines of therapy, including endocrine or cytotoxic agents; systemic treatment naive patients for metastatic disease are also eligible\r\n* Participants may initiate or continue bisphosphonate therapy on study\r\n* Continuation of ovarian suppression is allowed Completed all adjuvant therapy including (if indicated) endocrine, trastuzumab, radiation therapy Has received no more than previous lines of chemotherapy and has received at least one line of therapy with an endocrine therapy or endocrine therapy combination. Women with non-metastatic breast cancer with any hormone receptor and Her neu status who have completed surgery, chemotherapy, and radiation and are currently on endocrine therapy, single agent Herceptin, or observation Prior cancer therapy (except for endocrine therapy) must have been discontinued for week prior to initiation of study drugs Patients with ER+ breast cancer must have progressed on at least lines of endocrine therapy For estrogen receptor (ER)-positive breast cancer, patients must be considered refractory to endocrine therapy, having received and progressed through at least one prior line of endocrine therapy, or are intolerant of endocrine therapy Has received therapy for this current diagnosis of breast cancer including endocrine therapy or chemotherapy Concurrent adjuvant endocrine therapy and bone-modifying agents is allowed Subjects must be receiving endocrine therapy consisting of ) letrozole +/- palbociclib; or ) exemestane +/ everolimus; or ) fulvestrant +/- palbociclib; or ) anastrozole; or ) tamoxifen; pre-menopausal women must also be receiving a gonadotrophin releasing hormone (LHRH) agonist with endocrine therapy options through ; option can be used without LHRH agonists for pre-menopausal women Patients must have completed at least months of their current endocrine therapy prior to registration More than two prior endocrine therapy regimens for the treatment of metastatic ER+ breast cancer Patient must agree to the required research biopsies at baseline and after the two-week treatment with endocrine therapy in the initial part of the study (window phase); or at baseline and after two-week treated with endocrine therapy plus or minus palbociclib for those patients enrolled directly into the treatment phase of the study Patients are not eligible if they have previously received endocrine therapy within years prior to diagnosis of the current malignancy; this includes use for prophylactic reasons, including treatment of osteoporosis or cancer prevention with tamoxifen, raloxifene, or aromatase inhibitors (AI) Participants with endometrioid histology and histologically confirmed expression of estrogen receptors (ER) and/or progesterone receptors (PgR) who have not received prior endocrine therapy and for whom endocrine therapy is currently indicated. Breast cancer treatment for the currently diagnosed breast cancer including radiation therapy, chemotherapy, targeted therapy, or endocrine therapy prior to study registration Have received - lines of cytotoxic chemotherapy for metastatic breast cancer; prior endocrine therapy and/or targeted therapy is allowed Patients must have been treated with at least one prior chemotherapy regimen in the metastatic setting or within months of their last adjuvant systemic treatment and must be felt to be chemotherapy refractory; patients with ER positive disease must have demonstrated to be clinically endocrine-insensitive by progressing through at least one line of endocrine therapy, including approved combinations and considered candidate for more aggressive therapies (e.g. chemotherapy) per principal investigator (PI) or treating physician Candidate for neoadjuvant endocrine therapy Platelets >= ,/uL obtained no more than days prior to the start of neoadjuvant endocrine therapy Received any of the following for treatment of this cancer (except for the neoadjuvant endocrine therapy specified within this protocol):\r\n* Surgery\r\n* Radiation therapy\r\n* Chemotherapy\r\n* Biotherapy\r\n* Hormonal therapy\r\n* Investigational agent Unwilling to undergo anti-endocrine therapy Patient agrees to receive a year minimum course of endocrine therapy following cryoablation for control of systemic disease For HR+ breast cancer participants in part A, B, C, and F: If currently receiving endocrine therapy, a participant may continue to receive the same endocrine therapy provided that extracranial disease is stable for at least months and central nervous system (CNS) disease progression has occurred while on this endocrine therapy. If these conditions are not met, participants must discontinue endocrine therapy prior to initiation of abemaciclib. Corticosteroid therapy and endocrine replacement therapy (L-thyroxine, testosterone, estrogen, desmopressin acetate [DDAVP]) are permissible; any patient already receiving human growth replacement therapy should discontinue this prior to commencing chemotherapy, and should not restart until years from diagnosis Chemotherapy, radiation therapy, or biologic therapy (except trastuzumab) within days prior to initiating treatment on study; endocrine therapy and supportive therapy with bisphosphonates will be allowed Prior treatment with less than prior endocrine therapies for metastatic breast cancer Last dose of chemotherapy must be at least weeks before first dose of study treatment; there is no required washout for endocrine therapy Eligible for and willing to undergo a course of adjuvant endocrine therapy No limitations to number of prior chemotherapies for metastatic disease; treatment with prior taxanes (except nab-paclitaxel) is allowed as long as it has been months or more since exposure to prior taxane; NOTE: For subjects who are, or who have previously received endocrine therapy for breast cancer, the treating investigator will decide how many days should pass between the last dose of endocrine therapy and the first dose of study treatment Subjects should be > weeks from prior systemic chemotherapy for breast cancer AND should have recovered to grade or better (except alopecia) from related side effects of any prior antineoplastic therapy prior to study entry; NOTE: For subjects who are, or who have previously received endocrine therapy for breast cancer, the treating investigator will decide how many days should pass between the last dose of endocrine therapy and the first dose of study treatment Treatment including radiation therapy (RT), chemotherapy, targeted therapy, or endocrine therapy for the currently diagnosed breast cancer prior to randomization Patients must have had progressive disease after at least one line of endocrine therapy for metastatic disease (includes relapse while receiving endocrine therapy); there should be at least week interval between the last endocrine treatment for an aromatase inhibitor and at least weeks for tamoxifen or fulvestrant Patients must not have begun chemotherapy or endocrine therapy for their breast cancer prior to registration Step Registration must take place within days after definitive surgery; patients must not have begun chemotherapy or endocrine therapy for their breast cancer prior to randomization Patient may already have initiated adjuvant endocrine therapy (ET) at the time of randomization, but randomization must take place within weeks of date of initial histological diagnosis of breast cancer and within weeks of initiating ET may have received any endocrine therapy (excluding fulvestrant) There is no upper limit on prior chemotherapy, targeted therapy, or endocrine therapy relapsed with documented evidence of progression more than months from completion of (neo)adjuvant endocrine therapy and then subsequently; progressed with documented evidence of progression while on or after only one line of endocrine therapy for metastatic disease; Negative ?-human chorionic gonadotropin (hCG) pregnancy test for premenopausal women of reproductive capacity (those who are biologically capable of having children) and for women less than months after menopause. [Women are considered postmenopausal if they are ? months without menses, in the absence of endocrine or anti-endocrine therapies.] Oral endocrine therapy = and =< months from planned baseline visit date; in addition, participants must have completed local therapy (i.e. surgery and radiation therapy) and any planned preoperative or adjuvant chemotherapy within >= months prior to registration; NOTE: concurrent anti-human epidermal growth factor receptor (HER) therapy is permitted; concurrent endocrine breast cancer therapy is permitted; patients may enroll >= months after initiation of hormone therapy and if expected to continue the same endocrine/hormone agent for the duration of the study (i.e., care should be taken to ensure a participant enrolling near years since time of hormone treatment initiation will continue the same agent for at least months, switching hormone therapy on study should be avoided); concurrent enrollment in other interventional or drug clinical trials is at the discretion of the protocol chair Any number of prior endocrine therapies (including tamoxifen, fulvestrant and/or aromatase inhibitors in either the adjuvant or metastatic setting) and any number of prior chemotherapy regiments; anti-cancer systemic therapy, such as chemotherapy or biologics or endocrine therapy, other than the AI, must be discontinued for >= weeks prior to starting study treatment No limit on prior lines of endocrine therapy or biologic therapy; endocrine therapy and biologic therapy must be discontinued at least days prior to initiation of protocol therapy Breast cancer patients must be at least months post-active treatment (including chemotherapy, radiation therapy, endocrine therapy, and/or maintenance therapy), but not greater than years post-active treatment (exception: aromatase inhibitors (AIs) are required, and monoclonal antibodies are allowed) Endocrine resistant breast cancer, defined as either:\r\n* Relapsed while on adjuvant endocrine therapy or within year of completion of adjuvant endocrine therapy or\r\n* Progression through at least one line of endocrine therapy for metastatic or locally advanced breast cancer; there is no limit on the number of prior endocrine therapies received Concurrent treatment with commercial agents or other agents with the intent to treat the participants malignancy, including endocrine therapy, chemotherapy, and/or targeted therapy, with the exception of bisphosphonates and GnRH agonists Receiving concurrent endocrine, cytotoxic, or biologic agent(s) or within time limits specified above prior to study day If the participant is currently receiving or initiating standard adjuvant endocrine therapy at time of study entry, she/he must not have received more than weeks of adjuvant endocrine therapy following his/her last non-endocrine therapy (surgery, chemotherapy, or radiation). The participant has previously received endocrine therapy for breast cancer prevention (tamoxifen or raloxifene or aromatase inhibitors). Subjects must be receiving or be scheduled to receive standard of care systemic adjuvant or neoadjuvant chemotherapy and/or endocrine therapy and/or HER- targeted therapy Prior endocrine therapy for any histologically-confirmed cancer is not allowed; prior endocrine therapy that was administered >= years ago for the prevention of breast cancer in patients with no history of breast cancer is allowed There is no limit to the number of prior chemotherapy or endocrine therapy regimens allowed; patients with ER(+) AR(+) breast cancer must have had at least prior line of endocrine therapy to be eligible for the phase I portion of the trial Neoadjuvant endocrine monotherapy is deemed to be a suitable therapy. At least weeks since prior radiotherapy, endocrine therapy, trastuzumab, or lapatinib, with complete recovery from the effects of these interventions The patients may start any Food and Drug Administration (FDA) approved endocrine therapy (with which they have not been previously treated) at week of the trial except for tamoxifen Patients with metastatic disease currently on endocrine therapy must be willing to stop endocrine therapy for weeks prior to starting the study and to switch to a new endocrine therapy on the study (at week ) Can be on other endocrine therapy if willing to change a different endocrine therapy agent for the trial Must have at least one FDA approved endocrine therapy option with which the patient has not received prior treatment Patient has been treated with all FDA approved endocrine therapies or has been treated with all FDA approved endocrine therapies except for tamoxifen (tamoxifen is excluded from the trial) Patients must have had endocrine therapy initiated or planned for >= years; endocrine therapy can be given concurrently or following RT Patients treated with neoadjuvant chemo or endocrine therapy for breast cancer Participants with HR+/HER- breast cancer for whom endocrine-based therapy is considered an appropriate option per local clinical guidelines (i.e. participants should not be considered eligible for endocrine-based treatment) Evidence of progression to the combination of mTORi and endocrine therapy given as the last therapy prior to study entry Progression on or after endocrine treatment As per national or local treatment guidelines, endocrine therapy (i.e., fulvestrant) is recommended and treatment with cytotoxic chemotherapy is not necessary for participants, at time of entry into the study. Prior treatment with other chemotherapeutic agents, trastuzumab, endocrine and radiation therapy is permitted; Patient may already have initiated adjuvant endocrine therapy (ET) at the time of randomization, but randomization must take place within weeks of date of initial histological diagnosis of breast cancer and within weeks of initiating ET Completed definitive therapy consisting of surgery, chemotherapy or radiation therapy at least days ago (may continue on Herceptin or endocrine therapy) For breast cancer patients only, endocrine therapies are allowed (such as aromatase inhibitors, but not current tamoxifen. Prior tamoxifen is permitted with a day wash out period) Has received adjuvant endocrine therapy (selective estrogen receptor modulator [SERM] alone, gonadotropin-releasing hormone [GnRH] analogue plus SERM or aromatase inhibitors [AI]) for >= months but =< months for early breast cancer\r\n* Note: patients who have received neo/adjuvant endocrine treatment within a clinical trial and patients who have received pharmaco-prevention are eligible The adjuvant endocrine therapy must have stopped within month prior to enrollment Completion of all primary therapy (with the exception of ongoing endocrine or trastuzumab therapy), including surgery, radiation, and/or chemotherapy greater than weeks prior to study enrollment Have completed all surgery, radiation, and/or chemotherapy treatments at least months previously; may still be receiving trastuzumab or endocrine adjuvant therapy May use adjuvant endocrine therapy if use will be continued for duration of study intervention Stage I-III breast cancer\r\n* Treatment status: At least months and no more than years after the conclusion of active breast cancer therapy, including surgery, radiation therapy and (neo)adjuvant chemotherapy, if administered\r\n*NOTE: Adjuvant HER-targeted therapy and endocrine therapy may still be ongoing at the time of study enrollment; those on endocrine therapy must have been on their current endocrine regimen for at least four weeks prior to study enrollment and must not have plans to change endocrine regimens during the study period Concurrent endocrine therapy permissible Breast cancer survivors treated with chemotherapy with no evidence of disease with treatment completed at least six months prior to study participation with or without current endocrine therapy Women who are receiving endocrine therapy at the time of recruitment are eligible for the study Cases with stage I-IIIB breast cancer that have completed neoadjuvant or adjuvant treatment with anthracyclines and/or taxanes + or radiation therapy within past months (+/- days) (subjects on concurrent endocrine therapy [tamoxifen (TAM), aromatase inhibitors] are also eligible to participate) Completed active treatment (e.g., chemotherapy, radiation therapy, surgery) months- years\r\nago (current use of endocrine therapy is acceptable) Untreated endocrine abnormality, such as hypothyroidism, parathyroid hormone disorder No previous chemotherapy, endocrine, therapy or radiation therapy with therapeutic intent for this cancer Progression through at least one prior line of endocrine therapy Participant is scheduled to initiate treatment with everolimus combined with exemestane or another form of endocrine therapy Patients receiving systemic chemotherapy or radiation therapy within weeks of the start of everolimus (Note: there is no wash-out period for endocrine therapy) Concomitant trastuzumab and anti-endocrine therapies are permitted; if taking anti-endocrine therapy must have been taking for at least months prior to enrollment Participants who have received endocrine therapy within year prior to screening breast MRI >= months from all previous breast cancer treatment (including endocrine therapy) COHORT A: Diagnosis of breast cancer having completed any cytotoxic chemotherapy, radiation or surgery at least months prior to study entry; may continue to take endocrine therapy and/or maintenance trastuzumab At least months after completion of any cytotoxic chemotherapy or radiation or surgery; may continue to take endocrine therapy and/or maintenance trastuzumab Patients currently on endocrine therapy (tamoxifen, ralozifene or an aromatase inhibitor) May use adjuvant endocrine therapy if use will be continued for duration of study period Subjects with prior breast cancer must be off all systemic therapy (including endocrine agents) for at least years prior to registration Prior endocrine therapy with or without a CDK / inhibitor unless endocrine therapy is not indicated (ie, short relapse-free interval while on adjuvant endocrine therapy [endocrine resistance]; rapidly progressing disease/visceral crisis; or endocrine intolerance). Any targeted therapies approved for HER negative, HR positive MBC, including everolimus, are permitted as prior therapy. There is no limit to the number of prior endocrine therapies. Patients may enroll within years of breast cancer diagnosis, as long as there is a plan for at least more year of adjuvant endocrine therapy Participants must have been on adjuvant endocrine therapy, either tamoxifen or aromatase inhibitor (AI), for at least months without any significant adverse events leading to drug interruption for more than month, and must not have had any change in endocrine therapy in the past months; ongoing use of any AI, including letrozole, anastrozole or exemestane, or tamoxifen is allowed; concurrent gonadotrophin releasing hormone (GNRH) agonist is allowed Women who are receiving endocrine therapy for breast cancer treatment or chemoprevention including tamoxifen, letrozole, anastrozole, fulvestrant, or exemestane at the time of screening No history of receiving endocrine therapy, tamoxifen, and or aromatase inhibitors for therapeutic measures; these agents used previously as chemoprevention are allowed Patient is a postmenopausal woman, man, or premenopausal woman for whom standard endocrine therapy alone (tamoxifen, aromatase inhibitor [AI], with or without ovarian suppression or fulvestrant) is planned after FES-PET/CT is completed Patient must NOT be planning to receive molecular targeted therapy (such as everolimus or palbociclib) nor HER directed therapy in addition to endocrine therapy Patient must NOT have received prior endocrine therapy for metastatic disease (i.e., must be first-line endocrine therapy for metastatic disease) Patient is not now, and never has received adjuvant endocrine therapy OR patient is currently receiving or has received adjuvant endocrine therapy in the past, AND adjuvant endocrine therapy was initiated > years prior to diagnosis of metastatic disease\r\n* Note: patients who developed metastatic disease while still receiving adjuvant endocrine therapy must have a planned change in the type of endocrine agent used for subsequent metastatic disease treatment; patient is not receiving blocking adjuvant therapy (such as toremifene or tamoxifen) OR patient is receiving blocking adjuvant therapy, but will stop this therapy a minimum of days prior to FES-PET/CT while still complying with the study timeline Patients planning to receive neoadjuvant chemotherapy/endocrine therapy after the clinical breast MRI and before the research breast PET/MRI examination, those currently undergoing neoadjuvant chemotherapy/endocrine therapy, or those who have received chemotherapy/endocrine therapy within months prior to the MRI No prior endocrine therapy for metastatic disease is allowed (i.e. must be first-line endocrine therapy for metastatic disease). However, a history of adjuvant endocrine therapy is allowed, as long as the date of diagnosis of metastatic disease is > years following initiation of adjuvant endocrine therapy. Patients who develop metastatic disease while still receiving adjuvant endocrine therapy must have a change in the type of endocrine agent used for subsequent metastatic disease treatment. Patients on blocking adjuvant therapy (with a blocking agent such as toremifene or tamoxifen) must be off the agents for a minimum of days to allow for adequate uptake of FES. Postmenopausal women, men, or premenopausal women for whom endocrine therapy (tamoxifen, aromatase inhibitor [AI] with or without ovarian suppression or fulvestrant), with or without a CDK/ inhibitor is planned after FES-PET/CT is completed. Prior or chemotherapy or endocrine therapy is permitted History of progression or recurrence of disease while on an endocrine targeted therapy containing regimen as assessed by medical record review of breast cancer history at screening Patients planning to start new endocrine targeted therapy (any line of therapy is acceptable and any endocrine therapy is allowed) Patients must be selected for an endocrine targeted therapy regimen for treatment of their breast cancer by the referring oncologist; selected treatments may be part of experimental treatment protocols for which the patient would be separately consented Patients undergoing neoadjuvant endocrine therapy Received prior or ongoing local (e.g radiation) or systemic treatment (chemotherapy or endocrine therapy) for the current breast cancer; patients who received tamoxifen or raloxifene or another agent for prevention of breast cancer may be included as long as the patient has discontinued the treatment at least one month prior to baseline study biopsy Patients who have had any prior chemotherapy, radiotherapy, or endocrine therapy for the treatment of breast cancer. Patients may not be receiving any other investigational agents or any concomitant antineoplastic therapy, with the exceptions of octreotide long-acting release (LAR) (for neuroendocrine tumors) and endocrine therapy (for prostate, breast, or gynecologic malignancies) Must be candidates to receive endocrine therapy and palbociclib or ribociclib as first-line treatment for their advanced disease. Patients will be considered eligible for study enrollment if they have started on treatment with a standard dose and schedule of palbociclib or ribociclib and endocrine therapy (aromatase inhibitor or fulvestrant) as long as they have not started palbociclib or ribociclib treatment for longer than weeks from time of study enrollment, have sufficient tissue to perform the proposed tissue analysis and must meet all other eligibility criteria. Endocrine therapy can be initiated up to weeks prior to starting palbociclib or ribociclib. They have progressed on at least one previous line of endocrine therapy (ET) for\n their metastatic disease (but are not currently progressing on fulvestrant), OR;