A Study of Palbociclib in Combination With Bazedoxifene in Hormone Receptor Positive Breast Cancer

Inclusion Criteria: * Participants must have histologically confirmed invasive breast cancer that is metastatic or unresectable locally advanced. Histological documentation of metastatic/recurrent breast cancer is not required if there is unequivocal evidence for recurrence of the breast cancer. * Estrogen and/or progesterone receptor positive breast cancer (\>10% staining), as determined by pathology from either primary or metastatic site(s). Central confirmation is not required. * HER2 negative, defined as 0-1+ by immunohistochemistry or FISH-negative (HER2 copy number \<6 and HER2/CEP17 ratio \< 2.0). Central confirmation is not required. * Postmenopausal women are eligible. Postmenopausal is defined as any of the following: * Age ≥60 years * Age \<60 and amenorrhea for 12 or more months (in the absence of chemotherapy, tamoxifen, toremifen, or ovarian suppression) and FSH and estradiol in the postmenopausal range per local normal range. * Premenopausal women who have been on a GnRH agonist for at least 3 consecutive months prior to study entry are eligible. Women in this group MUST remain on the GnRH agonist for the duration of protocol treatment. * Status-post bilateral oophorectomy-After adequate healing post surgery. * Women, age ≥18 years of age. Men are excluded. * Because no dosing or adverse event data are currently available on the use of palbociclib and bazedoxifene in participants \<18 years of age, children are excluded from this study. In addition, breast cancer is exceedingly rare in individuals under 18 years of age. * Participants must have measurable disease by RECIST 1.1. See section 11 for the definition of measurable disease. * Bone only disease if there are lytic lesions is also allowed and treatment response will be evaluated based on the MD Anderson criteria. See section 11. * Endocrine resistant breast cancer, defined as either: * Relapsed while on adjuvant endocrine therapy or within 1 year of completion of adjuvant endocrine therapy \--- -or- * 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. * Patients may have received up to one prior line of chemotherapy for metastatic or unresectable locally advanced breast cancer. * Patients may have initiated bisphosphonate therapy prior to start of protocol therapy. Bisphosphonate therapy may continue during protocol treatment. Such patients will have bone lesions considered evaluable for progression * Patients must be at least 2 weeks from prior chemotherapy or radiotherapy, or any investigational drug product, with adequate recovery of toxicity to baseline, or grade \<1, with the exception of alopecia and hot flashes. There is no washout period for prior endocrine therapy. * ECOG Performance Status 0-1 (Appendix A) * Life expectancy of greater than 3 months * Willingness to undergo research biopsy under the following circumstances: * Patients with "easily accessible disease" * Patients with skin or chest wall disease amenable to a punch biopsy under local anesthesia are required to undergo a baseline biopsy and a biopsy at the time of disease progression as part of this protocol. * Patients with a breast mass or axillary lymph node amenable to an image-guided core biopsy are also required to undergo a baseline biopsy and a biopsy at the time of disease progression as part of this protocol. * Patients with malignant ascites fluid or a malignant pleural effusion of sufficient volume to be amenable to tap (either in-office or image-guided) are also required to undergo a baseline tap and a tap at the time of disease progression as part of this protocol. * Patients who undergo a research biopsy procedure for the purpose of this protocol, and in whom inadequate tissue is obtained, are still eligible and are not required to undergo a repeat biopsy in order to enter the study. * Patients will be approached during cycle 1 about providing an optional tissue sample at that time; however, this biopsy will be optional. * Patients with "accessible disease" * Patients with sites felt to be accessible to an image-guided or incisional biopsy in the opinion of the patient's treating oncologist and physician performing the procedure, and not meeting the criteria for "easily accessible disease" as described in Section 3.1.14.1, are required to undergo a baseline biopsy as part of this protocol. Such sites may include, but are not limited to: liver, lymph nodes, soft tissue, lung, chest wall, and bone. Cycle 1 biopsy and biopsy at time of disease progression are optional. * Biopsies may be done with local anesthesia or intravenous conscious sedation, according to standard institutional guidelines. * If a biopsy requires general anesthesia, then it is only allowed if acquisition of tissue is necessary for clinical reasons (i.e. is clinically indicated), and excess tissue that would otherwise have been discarded is then used for research purposes. If a biopsy requires general anesthesia, then a biopsy of that site for research purposes only, without a coexisting clinical indication is not allowed on this protocol. * Patients who undergo a research biopsy procedure for the purpose of this protocol, and in whom inadequate tissue is obtained, are still eligible and are not required to undergo a repeat biopsy in order to enter the study. * Some patients may have had a clinically indicated biopsy upon recent disease progression. No additional pre-treatment biopsy is required if that specimen can be used for the correlative studies described in this protocol. * Patients will be approached at the time of progression about providing an optional tissue sample at that time; however, the time of progression biopsy will be optional. * Other patients * Patients who do not have biopsy-accessible disease are not required to undergo a biopsy as part of study participation. * In addition, patients who are being treated with therapeutic doses of anticoagulant(s), are not required to undergo a biopsy as part of study participation. If it is felt clinically appropriate despite anticoagulation (i.e. a skin punch biopsy, etc) by the treating physician, a biopsy is allowed, it is simply not required. * The sites of metastatic disease and reason that the disease is not biopsy-accessible should be documented in the medical record and case report form(s). * Patients who do not undergo baseline biopsy must have their study participation approved by the overall PI before start of protocol therapy. Only patients who have biopsy inaccessible disease may enter the study without the requirement for baseline biopsy. * Participants must have normal organ and marrow function as defined below: * Absolute neutrophil count ≥1,500/mcL * Platelets ≥100,000/mcL * Hgb ≥9 mg/dL (which may be post transfusion) * Total bilirubin ≤1.5 X institutional upper limit of normal (patients with \---- documented Gilbert's disease are allowed total bilirubin up to 3X ULN) * AST (SGOT)/ALT (SGPT) ≤ 2.5 X institutional upper limit if no liver metastases; and ≤ 5 X institutional upper limit if liver metastases are present. * Creatinine ≤ 2X institutional upper limit of normal * Baseline QTc ≤ 480 ms * Ability to take oral medications. * The effects of palbociclib and bazedoxifene on the developing human fetus are unknown. If, for any reason, a woman should become pregnant or suspect that she is pregnant while participating in this study, she should inform her treating physician immediately. * Women who are made postmenopausal through use of GNRH agonists, and men are required to use adequate contraception for the duration of protocol treatment and for 6 months after the last dose of palbociclib and bazedoxifene. Adequate contraception is defined as one highly effective non-hormonal form of contraception or two effective forms of non-hormonal contraception by the patient and/or partner. * Highly Effective Non-Hormonal Contraception Methods of birth control which result in a low failure rate (i.e., less than 1% per year) when used consistently and correctly are considered highly-effective forms of contraception. The following non-hormonal methods of contraception are acceptable: * True abstinence when this is in line with the preferred and usual lifestyle of the patient. \[Periodic abstinence (e.g., calendar, ovulation, symptothermal post-ovulation methods) and withdrawal are not acceptable methods of contraception\]. * Male sterilization (with appropriate post-vasectomy documentation of the absence of sperm in the ejaculate). For female patients, the vasectomized male partner should be the sole partner. \--- OR * Effective Non-Hormonal Contraception Alternatively two of the following effective forms of contraception may be used instead: * Placement of non-hormonal intrauterine device (IUD) or intrauterine system (IUS). Consideration should be given to the type of device being used, as there is higher failure rates quoted for certain types, e.g., steel or copper wire. * Condom with spermicidal foam/gel/film/cream/suppository. * Occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository. The use of barrier contraceptives should always be supplemented with the use of spermicide. \- The following should be noted: * Failure rates indicate that, when used alone, the diaphragm and ondom are not highly effective forms of contraception. Therefore, the use of additional spermicides does confer additional theoretical contraceptive protection. * However, spermicides alone are ineffective at preventing pregnancy when the whole ejaculate is spilled. Therefore, spermicides are not a barrier method of contraception and should not be used alone. * It should be noted that two forms of effective contraception are required. A double barrier method is acceptable, which is defined as condom and occlusive cap (diaphragm or cervical/ vault caps) with spermicidal foam/gel/film/cream /suppository. Premenopausal women who have been on a GnRH agonist for at least 3 consecutive months prior to study entry are eligible. Women in this group MUST remain on the GnRH agonist for the duration of protocol treatment. Such patients should be counseled that GnRH agonists alone may not be adequate contraception and that adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation should be employed. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Prior treatment with a CDK4/6 inhibitor and/or bazedoxifene. * Participants may not be receiving any other investigational agents. * Concurrent treatment with commercial agents or other agents with the intent to treat the participant's malignancy, including endocrine therapy, chemotherapy, and/or targeted therapy, with the exception of bisphosphonates and GnRH agonists, as detailed in sections 3.1.4 and 3.1.9. * Untreated or progressive brain metastases. Patients with treated brain metastases not requiring chronic corticosteroids for symptom control are eligible. * Pending visceral crisis, in the opinion of the treating investigator. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to palbociclib and /or bazedoxifene. * Participants receiving any medications or substances that are strong inhibitors or inducers of CYP3A isoenzymes are ineligible. Lists including medications and substances known or with the potential to interact with the CYP3A isoenzymes are provided in Appendix D. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list such as http://medicine.iupui.edu/clinpharm/ddis/table.aspx; medical reference texts such as the Physicians' Desk Reference may also provide this information. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product. * Current use of drugs that are known to prolong the QT interval (See Appendix C) * Subjects with organ allograft requiring immunosuppression. * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Ability to comply with study requirements is to be assessed by each investigator at the time of screening for study participation. * Pregnant women are excluded from this study because effects of palbociclib and bazedoxifene on a developing fetus is unknown. Breastfeeding should be discontinued prior to entry onto the study. * Individuals with a history of a different malignancy are ineligible except for the following circumstances. Individuals with a history of other malignancies are eligible if they have been disease-free for at least 5 years and are deemed by the investigator to be at low risk for recurrence of that malignancy. Individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: ductal carcinoma in situ of the breast, cervical cancer in situ, and basal cell or squamous cell carcinoma of the skin. * Patients on combination antiretroviral therapy, i.e. those who are HIV-positive, are ineligible because of the potential for pharmacokinetic interactions or significant immunosuppression with Palbociclib.