A Study of Palbociclib in Combination With Fulvestrant or Tamoxifen as Treatment for Metastatic Breast Cancer

Inclusion Criteria: * Histologically or cytologically proven diagnosis of breast cancer with evidence of metastatic or locally advanced disease, not amenable to resection or radiation therapy with curative intent. * Patients 18 years of age or older, Female patients should be either: * Postmenopausal, as defined by at least one of the following criteria: * Age \>=60 years; * Age \<60 years and cessation of regular menses for at least 12 consecutive months with no alternative pathological or physiological cause; * Documented bilateral oophorectomy; * Medically confirmed ovarian failure. OR * Pre/peri-menopausal, ie, not meeting the criteria for being postmenopausal who are also receiving ongoing treatment with Luteinizing hormone-releasing hormone (LHRH) agonists (goserelin or leuprolide). The first injection should occur at least two weeks before study start. * Documentation of ER-positive and/or PR-positive tumor (≥1% positive stained cells) based on most recent tumor biopsy (unless bone-only disease,discuss with study PI if results are discordant) utilizing an assay consistent with local standards. * Documented human epidermal growth factor receptor 2 negative (HER2-) tumor based on local testing on most recent tumor biopsy: HER2-negative tumor is determined as immunohistochemistry score 0/1+ or negative by in situ hybridization (FISH/CISH/SISH) defined as a HER2/CEP17 ratio \<2 or for single probe assessment a HER2 copy number \<4. * Must have received prior treatment with an Mechanistic target of rapamycin (mTOR) or phosphatidylinositol 3-kinase (PI3K) inhibitor * Up to 2 prior lines of chemotherapy are allowed in the metastatic setting. * Any number of lines of prior hormone therapy are allowed * Patients with clear progression on either tamoxifen or fulvestrant should receive the alternate agent. Patients with clear progression on both drugs are not eligible. * Ability to have a skin and tumor biopsy. Patients without accessible tumor for biopsy will be considered on a case by case basis. * Patients who cannot be biopsied will not be replaced (although up to 5 ineligible/inevaluable patients can be replaced) * A patient without biopsy amenable tumor must be cleared by the PI of the study; up to 10 patients without biopsy amenable tumor will be allowed in each arm of the study. * Patients without accessible tumor for biopsy must provide archived tumor from the most recent biopsy available * Bone marrow, hepatic, and renal function as follows: Adequate bone marrow function: * leukocytes \> 2500/mL * absolute neutrophil count \> 1,000/mL * platelets \> 100,000/mL" Adequate hepatic function: * total bilirubin within normal institutional limits (unless Gilbert's disease with elevated indirect bilirubin only) * aspartate aminotransferase (AST) / (serum glutamic-oxaloacetic transaminase (SGOT) \< 2.5 X institutional upper limit of normal * alanine aminotransferase (ALT) / (serum glutamic-pyruvic transaminase (SGPT) \< 2.5 X institutional upper limit of normal * Adequate renal function: * creatinine within normal institutional limits * Measurable or evaluable disease as defined by RECIST version 1.1. Tumor lesions previously irradiated or subjected to other loco-regional therapy will only be deemed measurable if progression at the treated site after completion of therapy is clearly documented. * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Resolution of acute toxic effects of prior therapy or surgical procedures to National Cancer Institute (NCI) CTCAE Grade \<=1 (except alopecia) * Ability to understand a written informed consent document, and the willingness to sign it Exclusion Criteria: * Prior treatment with any cyclin-dependent kinase (CDK) inhibitor, and/or both fulvestrant and tamoxifen in the metastatic setting with clear progression. * Patients with advanced/metastatic, symptomatic, visceral spread, at risk of life-threatening complications in the short term by investigator assessment. * Known active uncontrolled or symptomatic central nervous system (CNS) metastases, carcinomatous meningitis, or leptomeningeal disease as indicated by clinical symptoms, cerebral edema, and/or progressive growth. Patients with a history of CNS metastases or cord compression are eligible if they have been definitively treated (eg, radiotherapy, stereotactic surgery) and are clinically stable off anticonvulsants and steroids for at least 4 weeks before randomization . * Current use of food or drugs known to be potent CYP3A4 inhibitors, drugs known to be potent CYP3A4 inducers (for examples, see the prohibited medications section), and drugs that are known to prolong the QT interval. See prohibited meds in appendix 5. * Major surgery, chemotherapy, radiotherapy, or other anti-cancer therapy within 2 weeks before randomization. * Any other malignancy within 3 years prior to randomization, except for adequately treated basal cell or squamous cell skin cancer, or carcinoma in situ of the cervix. * QTc interval \>480 msec (based on the mean value of the triplicate ECGs), family or personal history of long or short QT syndrome, Brugada syndrome or known history of QTc prolongation or Torsade de Pointes. QTc (Bazett) = QT/√RR * Any of the following within 6 months prior to study enrollment: myocardial infarction, severe/unstable angina, ongoing cardiac dysrhythmias of NCI CTCAE Grade \>=2, symptomatic congestive heart failure, or cerebrovascular accident excluding transient ischemic attack. * Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of palbociclib, such as history of GI surgery with may result in intestinal blind loops and patients with clinically significant gastroparesis, short bowel syndrome, unresolved nausea, vomiting, active inflammatory bowel disease or diarrhea of CTCAE v4.0 Grade \>1. * Prior hematopoietic stem cell or bone marrow transplantation. * Abnormalities in coagulation such as bleeding diathesis, or treatment with anticoagulants (that cannot be safely held for biopsy) that would preclude tumor and skin biopsies. * For fulvestrant: Ongoing anticoagulation that would preclude an IM injection * For tamoxifen: Documented hypercoagulable state not receiving anticoagulation * Known or possible hypersensitivity to palbociclib (CTCAE v4.0). * Known human immunodeficiency virus infection. * Other severe acute or chronic medical or psychiatric condition, including recent or active suicidal ideation or behavior, or laboratory abnormality that may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for entry into this study. * Participation in other studies involving investigational drug(s) (Phases 1-4) within 2 weeks before randomization the current study. * Women should not become pregnant or breastfeed whilst on this study. Birth control methods are acceptable and will be discussed with study participants.