Palbociclib in Treating Patients With Metastatic HER-2 Positive Breast Cancer With Brain Metastasis

Inclusion Criteria: * Histologically confirmed HER2-positive metastatic breast cancer (estrogen and progesterone receptor 0%, HER-2 3+ by immunohistochemistry (IHC); if IHC score of 2, fluorescence in situ hybridization (FISH) ratio must be greater than 2.0; if FISH less than 2.0, HER2 copy number must be greater than 6; NOTE: Brain lesions are not required to have pathologic confirmation * Patients should not have received \> 2 lines of chemotherapy for metastatic disease * Patients must have a life expectancy of at least 12 weeks at the time of registration * Eastern Cooperative Oncology Group (ECOG) performance status \>= 2 * Measurable disease in the brain, defined as at least 1 lesion measuring \>= 5 mm on imaging at the time of registration * If patients are on corticosteroids, they must have been on a stable or decreasing dose \>= 5 days prior to obtaining their baseline gadolinium (Gd)-magnetic resonance imaging (MRI) of brain; this MRI is to be obtained within 28 days of registration; NOTE: If patient needs escalation of steroids prior to therapy, or are on unstable doses of steroids they are not eligible * Patients who underwent neurosurgery (NSGY) or stereotactic radiosurgery (SRS) to a brain lesion must have a new measureable lesion; NOTE: SRS may be done to a lesion that will not be used for response evaluation and should be done \> 2 weeks prior to registration; any NSGY procedure must have been completed \> 3 weeks prior to registration * Patients must not have received systemic therapy within 2 weeks of initiating palbociclib; NOTE: For the HER2-positive cohort, patients on trastuzumab can remain on the drug; no break or washout period required; however, lapatinib, ado-trastuzumab-emtansine, and pertuzumab are prohibited and a minimum wash out period of 2 weeks is required * Patients must exhibit adequate bone marrow, liver, and renal function, within 14 days prior to registration, defined as: * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 (growth factor support is permitted) * Platelets \>= 100,000/mm\^3 (may be reached by transfusion) * Hemoglobin \>= 10 gm/dl (may be reached by transfusion) * Glutamate pyruvate transaminase (GPT)/glutamate oxaloacetate transaminase (GOT) \< 3 x upper limit of normal (ULN) (or \< 5 x ULN in case of liver metastasis) * Bilirubin \< 3 x ULN (or \< 5 x ULN in case of liver metastasis) * Creatinine \< 1.5 x ULN * Females of child-bearing potential (FOCBP) and males must agree to use adequate contraception prior to study entry, for the duration of study participation, and for 2 weeks following completion of therapy; should a female patient become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately; likewise, if the female partner of a male patient becomes pregnant while participating in this study, he should inform his treating physician immediately; NOTE: A FOCBP is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy * Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for \> 12 months) * Female patients must have a negative urine pregnancy test within 7 days prior to registration; if urine test is positive, it should be followed by serum pregnancy test * Patients must sign an informed consent prior to registration and before undergoing any study-specific procedures indicating that they are aware of the investigational nature of this study * Patient must have the ability to swallow and retain oral medication * Patient must have the ability to comply with all study requirements Exclusion Criteria: * Any uncontrolled neurological symptom attributed to CNS metastasis * Brain metastasis must not be impending herniation or other significant vasogenic edema requiring increasing steroid doses; lesions must not have frank hemorrhage * Patients with leptomeningeal disease are not eligible for participation * Any significant medical illnesses or infection that, in the investigator's opinion, cannot be adequately controlled with appropriate therapy or would compromise the patient's ability to tolerate this therapy are not eligible for participation * Known human immunodeficiency virus (HIV) positive status * Known active hepatitis B and/or C * Previous treatment with palbociclib * Patients who have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to palbociclib are not eligible; AND/OR patients who have had prior exposure to compounds of similar chemical or biologic composition to palbociclib are not eligible hypersensitivity to any component of palbociclib are not eligible for participation * Patients being treated with any other experimental agents/clinical trials are not eligible for participation; if the patient is on any investigational agent, a wash-out period of minimum 2 weeks prior to registration is mandatory for the patient to be eligible for the study * Patients who are on any prohibited medication; a wash-out period of minimum 2 weeks prior to registration is mandatory for the patient to be eligible for the study * Inability to swallow capsules, malabsorption syndrome or gastrointestinal disease that severely affects the absorption of study drugs, major resection of the stomach or small bowel, or gastric bypass procedure * Patients who have an uncontrolled intercurrent illness including, but not limited to any of the following, are not eligible: * Ongoing or active infection requiring systemic treatment * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia: except atrial fibrillation (AF) and supraventricular tachycardia (SVT) that are controlled by medication * Psychiatric illness/social situations that would limit compliance with study requirements * Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints * Female patients who are pregnant or nursing are not eligible