Inclusion Criteria:
 - -  Participants must have histologically or cytologically confirmed disease from any
     solid tumor (Cohort 1)
  -  Participants must have histologically or cytologically confirmed disease from breast
     cancer (Cohort 2).
- -  Participants must have measurable disease in the CNS, defined as at least one lesion
     that can be accurately measured in at least one dimension as ≥10 mm.
- -  Participants must have progressive CNS lesions, as defined by one of the following:
       -  Patients may have multiple progressive CNS lesions, some of which have been
          treated by SRS or surgery.
Patients are eligible if they have one or more
          un-treated (by surgery or SRS) progressive lesions that is measurable.
      
- -  Patients have measurable residual or progressive lesions after surgery.
- -  Patients who have had prior WBRT and/or SRS are eligible but there needs to be
          unequivocal evidence of progression of at least one lesion treated by radiation
          (e.g. tissue diagnosis).
Biopsy can be considered for definitive diagnosis.
      
- -  Patients who have previously been treated with systemic therapy for CNS
          metastases are eligible.
The toxicity of palbociclib in children is unknown.
 
- -  ECOG performance status of 0, 1 or 2 (Karnofsky ≥ 60, see Appendix A).
- -  Participants must have normal organ and marrow function as defined below:
       -  leukocytes ≥3,000/mcL.
- -  absolute neutrophil count ≥1,500/mcL.
- -  platelets ≥100,000/mcL.
- -  total bilirubin < 1.5 x institutional upper limit of normal OR > 1.5 x
          institutional upper limit of normal allowed if direct bilirubin is within
          normal range.
- -  AST(SGOT)/ALT(SGPT) ≤2.5 × institutional upper limit of normal.
- -  creatinine within normal institutional limits OR.
- -  creatinine clearance ≥60 mL/min/1.73 m2 for participants with creatinine
               levels above institutional normal (Cohort 1)
            -  creatinine clearance ≥30 mL/min/1.73 m2 for participants with creatinine
               levels above institutional normal (Cohort 2)
       -  baseline QTc <480ms.
- -  The effects of palbociclib on the developing human fetus are unknown.
For this
     reason, women of child-bearing potential and men must agree to use adequate
     contraception (hormonal or barrier method of birth control; abstinence) prior to
     study entry and for the duration of study participation. Should a woman become
     pregnant or suspect she is pregnant while she or her partner is participating in
     this study, she should inform her treating physician immediately. Men treated or
     enrolled on this protocol must also agree to use adequate contraception prior to the
     study, for the duration of study participation, and 6 months after completion of
     palbociclib administration.
 
- -  Ability to understand and the willingness to sign a written informed consent
     document.
- -  Tissue from a prior biopsy or resection of intracranial or extracranial site
     (primary or metastatic site) for clinical genetic sequencing (at least one FFPE
     block or 15 unstained slides).
Patients previously assessed for genetic sequencing
     who meet requirements of section 9.2.1 do not need to have additional tissue
     available for prospective genetic screening.
 
- -  Presence of alteration in CDK pathway in any biopsy or resection (amplifications in
     CDK4, CDK6, CCND1, CCND2, CCND3 or CCNE1 or loss of CDKN2A) as described in Section
     9.2 using a CLIA-certified assay (Cohort 1 only).
- -  Patients with progressive extracranial disease will not be excluded.
- -  Stable dose of corticosteroids for at least 7 days.
- -  Participants who are HBsAg positive are eligible if they have received HBV
     anti-viral therapy for at least 4 weeks, and have undetectable HBV viral load prior
     to enrollment.
- -  Note: Participants should remain on anti-viral therapy throughout study
          intervention and follow local guidelines for HBV anti-viral therapy post
          completion of study intervention.
- -  Hepatits B screening tests are not required unless:
            -  Known history of HBV infection.
- -  As mandated by local health authority.
- -  Participants with a history of HCV infection are eligible if HCV viral load is
     undetectable at screening.
- -  Note: Participants must have completed curative anti-viral therapy at least 4
          weeks prior to enrollment.
- -  Heptatits C screening tests are not required unless:
            -  Known history of HCV infection.
- -  As mandated by local health authority.
Exclusion Criteria. 
- -  Prior treatment with CDK4/6 inhibitor.
- -  Participants who have had chemotherapy, immunotherapy or radiotherapy within 2 weeks
     (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who
     have ≥ grade 2 adverse events due to agents administered more than 2 weeks earlier.
- -  Participants who are receiving any other investigational agents.
- -  Participants who are receiving other concurrent chemotherapies or immunotherapies
     for their cancer (except for patients who will receive letrozole, anastrozole,
     exemestane, tamoxifen, fulvestrant, trastuzumab, bisphosphonates, or ovarian
     suppression therapy)
  -  Leptomeningeal involvement of cancer (Cohort 1).
Leptomeningeal involvement is
     allowed for Cohort 2.
 
- -  History of allergic reactions attributed to compounds of similar chemical or
     biologic composition to palbociclib (including abemaciclib).
- -  Participants receiving any medications or substances that are moderate or 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 C, and can also be found within section 5.4.
     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.
 
- -  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.
- -  Pregnant women are excluded from this study because the effect of palbociclib on a
     developing fetus is unknown.
Because there is an unknown but potential risk for
     adverse events in nursing infants secondary to treatment of the mother with
     palbociclib, breastfeeding should be discontinued if the mother is treated with
     palbociclib.
If a participant inadvertently becomes pregnant while on treatment with pembrolizumab,
the participant will be immediately discontinued from study intervention(s). The site
will contact the participant at least monthly and document the participant's status until
the pregnancy has been completed or terminated. The outcome of the pregnancy will be
reported to Merck within 2 working days if the outcome is a serious adverse experience
(e.g. death, abortion, congenital anomaly, or other disabling or life-threatening
complication to the mother or newborn). The study Investigator will make every effort to
obtain permission to follow the outcome of the pregnancy and report the condition of the
fetus or newborn to Merck. If a male participant impregnates his female partner, the
study personnel at the site must be informed immediately and the pregnancy must be
reported to the Overall PI, Merck and Pfizer and followed as necessary.
 
- -  HIV-positive participants on combination antiretroviral therapy are ineligible
     because of the potential for pharmacokinetic interactions with palbociclib.
In
     addition, these participants are at increased risk of lethal infections when treated
     with marrow-suppressive therapy. Appropriate studies will be undertaken in
     participants receiving combination antiretroviral therapy when indicated (Cohort 1).
     In Cohort 2, HIV-positive patients will NOT be permitted.
 
- -  Current use of drugs that are known to prolong the QT interval (See Appendix C).
- -  Unable to undergo MRI scans.
- -  QTc > 480 msec (based on the mean value of the triplicate ECGs), family or personal
     history of long or short QTc prolongation, or Torsade de Pointes (TdP).
- -  Uncontrolled electrolyte disorders that can compound the effects of QTc-prolonging
     drug (eg.
hypocalcemia, hypokalemia, hypomagnesemia).
 
- -  Active auto immune disease (Cohort 2)
  -  Patients with history of lung radiation (Cohort 2)
  -  Prior treatment with PD-1 or PD-L1 blocking agent (Cohort 2)
  -  History of allogenic transplant.
- -  History of (non-infectious) pneumonitis/interstitial lung disease that required
     steroids or has current pneumonitis/interstitial lung disease.
-  History of Hepatitis B or known active Hepatitis C virus infection