ONC201 in Recurrent/Refractory Metastatic Breast Cancer and Advanced Endometrial Carcinoma

* INCLUSION CRITERIA FOR COHORT 1: HORMONE RECEPTOR POSITIVE BREAST CANCER: * Patients must have histologically confirmed persistent or recurrent invasive metastatic hormone receptor positive, human epidermal growth factor receptor 2 (HER2) normal breast cancer for which standard curative measures do not exist or are no longer effective. Hormone receptor positive is defined as estrogen receptor (ER) positive greater than or equal to 10% by immunohistochemistry (IHC) and/or progesterone receptor (PR) positive greater than or equal to 10% by IHC.HER2 will be considered negative per American Society of Clinical Oncology (ASCO)-College of American Pathologists (CAP) guidelines (HER2 test result as negative if a single test (or both tests) performed show: 1) IHC 1+ as defined by incomplete membrane staining that is faint/barely perceptible and within \>10% of the invasive tumor cells; 2) IHC 0 as defined by no staining observed or membrane staining that is incomplete and is faint/barely perceptible and within less than or equal to 10% of the invasive tumor cells; or 3) ISH negative based on: a) Single-probe average HER2 copy number \<4.0 signals/cell or b) Dualprobe HER2/ chromosome enumeration probe 17 (CEP17) ratio \<2.0 with an average HER2 copy number \<4.0 signals/cell)and HER2 testing must have been performed in a laboratory accredited by the College of American Pathologists (CAP) or another accrediting entity. * Patients must have measurable disease, per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. * Patients must have at least one lesion deemed safe to biopsy and be willing to undergo mandatory biopsies. * Hormone receptor + breast cancer (HR+BC) patients must have received prior treatment with at least 2 lines of hormonal treatment (Selective estrogen receptor modulators (SERM), aromatase inhibitor (AI), or fulvestrant) and deemed ineligible for further hormonal therapy. Patients may have received prior chemotherapy and there is no limit to the number of prior chemotherapy. * Age greater than or equal to18 years. * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Adequate renal function, defined as serum creatinine less than or equal to 1.5 X upper limit of normal (ULN), or measured creatinine clearance greater than or equal to 60 mL/min/1. * Adequate hepatic function, defined as aspartate aminotransferase (AST) and alanine aminotransferase (ALT) levels less than or equal to 3 X ULN and total bilirubin \< 1.5 X ULN, unless known diagnosis of Gilbert's syndrome, where bilirubin less than or equal to 5 mg/dL will be permitted. Gilbert's syndrome will be defined as elevated unconjugated bilirubin, with conjugated (direct) bilirubin within the normal range and less than 20% of the total. Total bilirubin will be permitted up to 5 mg/dL, if patients have historical readings consistent with the definition of Gilbert's syndrome prior to entering study. * Adequate bone marrow function, defined as absolute neutrophil (ANC) greater than or equal to 1,500/mm\^3 (greater than or equal to 1.5 X10\^6/L), platelet count greater than or equal to 75,000/mm\^3 (greater than or equal to 75 X10\^6/L), and hemoglobin greater than or equal to 9 mg/dL (transfusion to obtain hemoglobin greater than or equal to 9 mg/dL within 24 hours prior to dosing is allowed). * Patients must be able to swallow oral medications (capsules) without chewing, breaking, crushing, opening or otherwise altering the product formulation. * The effects of ONC201 on the developing human fetus are unknown. For this reason and because imipridone agents are known to be teratogenic, female patients must either be of non-reproductive potential (i.e., post-menopausal by history: greater than or equal to 60 years old and no menses for greater than or equal to 1 year without an alternative medical cause; OR history of hysterectomy, OR history of bilateral tubal ligation, OR history of bilateral oophorectomy) or must have a negative serum pregnancy test upon study entry and agree to use contraception or abstinence during the study and for and for at least 4 weeks after the final dose of any study-related medications. Male patients must use at least two forms of contraception during the study and for at least 4 weeks after the final dose of any study-related medications or have a partner who is not of reproductive potential. * Ability of subject to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA FOR COHORT 1: HORMONE RECEPTOR POSITIVE BREAST CANCER: * Patients who have received chemotherapy in the previous 3 weeks (6 weeks for nitrosoureas or mitomycin); other investigational agents within 3 weeks or a programmed cell death protein 1 (PD1)/programmed death-ligand 1 (PDL1) agent within 4 weeks prior to first dose of study enrollment. * Patients who have undergone radiotherapy within 4 weeks of first dose of study treatment. * Patients with a history of another invasive malignancy within the last 3 years. * Patients with symptomatic brain metastases or leptomeningeal involvement. Patients with asymptomatic or brain metastases that have been treated with radiation at least 4 weeks prior to first dose of study treatment are allowed. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to imipridones or other agents used in study. * Patients with a mean corrected Q wave T wave (QT) interval by Fridericia (QTcF) interval of \> 500 msec or receiving therapeutic agents known to prolong the QT interval * Known history of cardiac arrhythmias including uncontrolled atrial fibrillation, tachyarrhythmias or bradycardia, history of congestive heart failure, or myocardial infarction or stroke in the previous 3 months will be excluded. * Known history of gastrointestinal illnesses that would preclude the absorption of ONC201, which is an oral agent. * Patients with bone metastases who have initiated denosumab or bisphosphonate therapy within 28 days prior to Cycle 1 Day 1. * Pregnant women are excluded from this study because ONC201 has the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with ONC201, breastfeeding should be discontinued if the mother is treated with ONC201. These potential risks may also apply to other agents used in this study. * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with ONC201. * Patients who have known active Hepatitis B, or Hepatitis C infections. INCLUSION CRITERIA FOR COHORT 2: TRIPLE NEGATIVE BREAST CANCER: * Patients must have histologically or cytologically confirmed persistent or recurrent invasive, metastatic triple negative breast cancer (TNBC) for which standard curative measures do not exist or are no longer effective. TNBC, defined as estrogen receptor (ER) negative (ER \< 10%), PR negative (PR \<10%). HER2 will be considered negative per ASCO-CAP guidelines (HER2 test result as negative if a single test (or both tests) performed show: 1) IHC 1+ as defined by incomplete membrane staining that is faint/barely perceptible and within \>10% of the invasive tumor cells; 2) IHC 0 as defined by no staining observed or membrane staining that is incomplete and is faint/barely perceptible and within less than or equal to 10% of the invasive tumor cells; or 3) ISH negative based on: a) Single-probe average HER2 copy number \<4.0 signals/cell or b) Dual-probe HER2/CEP17 ratio \<2.0 with an average HER2 copy number \<4.0 signals/cell) and HER2 testing must have been performed in a laboratory accredited by the College of American Pathologists (CAP) or another accrediting entity. * Patients must have received at least one line of prior chemotherapy in the metastatic setting. * Patients must have measurable disease, per RECIST 1.1. * Patients must have at least one lesion deemed safe to biopsy and be willing to undergo mandatory biopsies. * Eligible patients may or may not have received prior chemotherapy and there is no limit to the number of prior chemotherapy. Patients are also eligible if they have received treatment with immunotherapy, such PD-1 inhibitors, PD-L1 inhibitors or cytotoxic T-lymphocyte-associated antigen 4 (CTLA-4) inhibitors. * Age greater than or equal to 18 years. * ECOG performance status 0 or 1 * Adequate renal function, defined as serum creatinine less than or equal to 1.5 X upper limit of normal (ULN), or measured creatinine clearance greater than or equal to 60 mL/min/1. * Adequate hepatic function, defined as AST and ALT levels less than or equal to 3 X ULN and total bilirubin \< 1.5 X ULN, unless known diagnosis of Gilbert's syndrome, where bilirubin less than or equal to 5 mg/dL will be permitted. Gilbert's syndrome will be defined as elevated unconjugated bilirubin, with conjugated (direct) bilirubin within the normal range and less than 20% of the total. Total bilirubin will be permitted up to 5 mg/dL, if patients have historical readings consistent with the definition of Gilbert's syndrome prior to entering study. * Adequate bone marrow function, defined as absolute neutrophil (ANC) greater than or equal to 1,500/mm\^3 (greater than or equal to 1.5 X10\^6/L), platelet count greater than or equal to 75,000/mm\^3 (greater than or equal to 75 X10\^6/L), and hemoglobin greater than or equal to 9 mg/dL (transfusion to obtain hemoglobin greater than or equal to 9 mg/dL within 24 hours prior to dosing is allowed) * Patients must be able to swallow oral medications (capsules) without chewing, breaking, crushing, opening or otherwise altering the product formulation. * The effects of ONC201 on the developing human fetus are unknown. For this reason and because imipridone agents as well as other therapeutic agents used in this trial are known to be teratogenic. Female patients must either be of non-reproductive potential (i.e., post-menopausal by history: greater than or equal to 60 years old and no menses for greater than or equal to 1 year without an alternative medical cause; OR history of hysterectomy, OR history of bilateral tubal ligation, OR history of bilateral oophorectomy) or must have a negative serum pregnancy test upon study entry and agree to use contraception or abstinence during the study and for and for at least 4 weeks after the final dose of any study-related medications. Male patients must use at least two forms of contraception during the study and for and for at least 4 weeks after the final dose of any study-related medications or have a partner who is not of reproductive potential. * Ability of subject to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA FOR COHORT 2: TRIPLE NEGATIVE BREAST CANCER: * Patients who have received chemotherapy in the previous 3 weeks (6 weeks for nitrosoureas or mitomycin); other investigational agents within 3 weeks or a PD1/PDL1 agent within 4 weeks prior to first dose of study treatment. * Patients who have undergone radiotherapy within 4 weeks of first dose of study treatment. * Patients with a history of another invasive malignancy within the last 3 years. * Patients with symptomatic brain metastases or leptomeningeal involvement. Patients with asymptomatic or brain metastases that have been treated with radiation at least 4 weeks prior to first dose of study treatment are allowed. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to imipridones or other agents used in study. * Patients with a mean QTcF interval of \> 500 msec or receiving therapeutic agents known to prolong the QT interval * Known history of cardiac arrhythmias including uncontrolled atrial fibrillation, tachyarrhythmias or bradycardia, history of congestive heart failure, or myocardial infarction or stroke in the previous 3 months will be excluded. * Known history of gastrointestinal illnesses that would preclude the absorption of ONC201, which is an oral agent * Patients with bone metastases who have initiated denosumab or bisphosphonate therapy within 28 days prior to Cycle 1 Day 1. * Pregnant women are excluded from this study because ONC201 has the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with ONC201, breastfeeding should be discontinued if the mother is treated with ONC201. These potential risks may also apply to other agents used in this study. * HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with ONC201. * Patients who have known active Hepatitis B, or Hepatitis C infections. INCLUSION CRITERIA FOR COHORT 3: ENDOMETRIAL CANCER: * Patients must have histologically or cytologically confirmed persistent or recurrent advanced or metastatic invasive endometrial cancer (EC) for which standard curative measures do not exist or are no longer effective. * Patients must have measurable disease, per RECIST 1.1 * Patients must have at least one lesion deemed safe to biopsy and be willing to undergo mandatory biopsies. * Women with endometrial cancer must have had at least one prior line of therapy in the metastatic/recurrent setting but there is no limit to the number of prior chemotherapy lines. Patients are eligible if they have received treatment with immunotherapy, such PD-1 inhibitors, PD-L1 inhibitors or CTLA4 inhibitors. * Age greater than or equal to 18 years. * ECOG performance status 0 or 1 * Adequate renal function, defined as serum creatinine less than or equal to 1.5 X upper limit of normal (ULN), or measured creatinine clearance greater than or equal to 60 mL/min/1. * Adequate hepatic function, defined as AST and ALT levels less than or equal to 3 X ULN and total bilirubin \< 1.5 X ULN, unless known diagnosis of Gilbert's syndrome, where bilirubin less than or equal to 5 mg/dl will be permitted. Gilbert's syndrome will be defined as elevated unconjugated bilirubin, with conjugated (direct) bilirubin within the normal range and less than 20% of the total. Total bilirubin will be permitted up to 5 mg/dL, if patients have historical readings consistent with...