Palbociclib and Pembrolizumab in Sarcoma

Inclusion Criteria A potential subject must meet all the following inclusion criteria to be eligible to participate in the study: * Male or female patients aged \> or = 12 years old * ECOG Performance Status of \< or = 2 * Any patient with the diagnosis of locally advanced, unresectable or metastatic sarcoma for which PD-1 inhibitors are approved (undifferentiated pleomorphic sarcoma, myxofibrosarcoma, angiosarcoma, pleomorphic rhabdomyosarcoma, pleomorphic liposarcoma, alveolar soft part sarcoma) who have progressed on at least 1 prior line of therapy. Prior immunotherapy treatment is allowed, including prior treatment with a PD-1 inhibitor. * Patients with no known CNS disease, except for treated brain metastasis. Treated brain metastases are defined as having no evidence of progression or hemorrhage after treatment and no ongoing treatment for dexamethasone (as ascertained by clinical examination and brain imaging) during the screening period. Stable dose of anticonvulsants is allowed. Treatment for brain metastases may include whole brain radiotherapy, radiosurgery, or a combination as deemed appropriate by the treating physician. Patients with CNS metastases treated by neurosurgical resection or brain biopsy performed within 3 months prior to Day 1 will be excluded. * Ability to understand and the willingness to sign a written informed consent or assent in case of patients \< 18 years old. Exclusion Criteria A potential subject who meets any of the following exclusion criteria is ineligible to participate in the study: * Lab values in the below ranges: * Neutrophil count \< 1000/mm3 * Platelet count \< 100,000/mm3L * Hemoglobin \< 9 g/dL (transfusion to meet eligibility allowed) * AST/SGOT and ALT/SGPT \> 3.0x upper limit of normal (ULN) without disease involvement or \> 5.0x ULN if the transaminase elevation is due to disease involvement * Alkaline phosphatase \> 5.0x ULN without known bony metastases * Serum bilirubin \> 1.5x ULN * Serum creatinine \> 1.5x ULN or 24-hour creatinine clearance \< 30 mL/min per Cockroft- Gault equation * Total serum calcium \< lower limit of normal (LLN) or if calcium is below LLN the corrected calcium for serum albumin is \> LLN * Serum potassium \< 3.0 * Serum sodium \< 130 * Serum albumin \< 2.5 g/dL * History of myocardial infarction. unstable angina, stroke or transient ischemic attack within 6 months prior to Day 1 * History or drug induced pneumonitis (both pembrolizumab and palbociclib can cause pneumonitis) * Subjects requiring hemodialysis * Patients with severe hepatic impairment (Childs-Pugh Class C). * Other concurrent severe and/or uncontrolled medical conditions in the opinion of the investigator which will preclude participation * Pregnancy (positive pregnancy test) or lactation * Concomitant use of any other anti-cancer therapy or radiation therapy of the target lesion. Palliative radiation therapy is permitted to non-target lesions. * Patients with any significant history of non-compliance to medical regimens or with inability to grant a reliable informed consent