Inclusion Criteria:

          1. Over-expression of CDK4 (mRNA expression) and a low-to-normal p16 expression (mRNA
             expression) measured in paraffin embedded tumor samples at study entry.

          2. ECOG 0-1 at enrollment.

          3. Diagnosis of soft tissue sarcoma or osteosarcoma (in both cases with metastasis or
             locally advanced, unresectable).

          4. Disease progression documented within 6 months prior to study entry.

          5. Patients must have the following laboratory results:

               -  ANC ≥ 1,500/mm3 (1.5 x 109/L);

               -  Platelets ≥ 100,000/mm3 (100 x 109/L);

               -  Hemoglobin ≥ 9 g/dL (90 g/L);

               -  Serum creatinine ≤ 1.5 x ULN or estimated creatinine clearance ≥ 60 mL/min;

               -  Total serum bilirubin ≤ 1.5 x ULN (≤ 3.0 x ULN if Gilbert's disease);

               -  AST and/or ALT ≤ 3 x ULN (≤ 5.0 x ULN if liver metastases present);

               -  Alkaline phosphatase ≤ 2.5 x ULN (≤ 5.0 x ULN if bone or hepatic metastasis
                  present);

          6. Patients must have signed written informed consent to participate in the clinical
             study, and to provide at least two paraffin embedded tumor blocks for the molecular
             analyses at screening stage.

          7. Biopsy at baseline if there are no archived tumor samples obtained within 3 months
             prior to treatment initiation.

          8. Patients must have received standard treatments for at least one, two or three lines
             for advanced disease.

          9. Age between 18 and 80 years (both ages included).

         10. Measurable disease according to RECIST 1.1 criteria.

         11. All patients (men and women) in fertile age must use an effective contraception method
             during the entire treatment with palbociclib and for at least 90 days after the last
             dose. Pregnancy must be ruled out through urine or blood test (negative pregnancy
             test) for the inclusion in the study. Men must be informed to consider spermatic
             preservation before treatment initiation due to infertility risks.

        Exclusion Criteria:

          1. Previous treatment with any anti CDK4 or immune checkpoint inhibitor.

          2. Diagnosis of Ewing sarcoma or rhabdomyosarcoma.

          3. Diagnosis of well differentiated/dedifferentiated liposarcoma.

          4. Patients irradiated on the only target lesion available.

          5. Patients having received more than three lines for advanced disease.

          6. History of other neoplastic disease with the exception of basal cell carcinoma or in
             situ cervical cancer adequately treated.

          7. Serious cardiovascular disease (NYHA >= 2)

          8. Grade 3 or superior toxicity according to CTCAE 4.0 if the investigator considers this
             can significantly interfere in the toxicity of the drug under study.

          9. Patients not recovered from a previous toxicity to at least CTCAE Grade 1 due to prior
             chemotherapy, radioactive, or biological cancer therapy (including monoclonal
             antibodies).

         10. Patients not recovered from minor or major surgery or having undergone a major surgery
             within the last 4 weeks prior to initiation of study treatment.

         11. Central nervous system metastasis.

         12. Pregnant or breastfeeding patients, or those expecting to conceive or father children
             within the projected duration of treatment.

         13. Foods or drugs known as CYP3A4 inhibitors/inducers; CYP3A4 substrates with narrow
             therapeutic windows, or known to prolong QTc interval.

         14. Major surgery, chemotherapy, radiotherapy, any agent under investigation, or other
             antineoplastic therapy within 4 weeks prior to inclusion. Patients having received a
             previous radiotherapy ≥25% of bone marrow are not eligible, regardless of when it was
             received.

         15. QTc > 480 ms; personal or family history of long or short QT syndrome, Brugada
             syndrome or known history of QTc prolongation, or Torsades de Pointes (TdP).

         16. Any of the following situations within 6 months prior to study drug administration:
             myocardial infarction, serious/unstable angina, current cardiac dysrhythmias Grade ≥ 2
             NCI-CTCAE version 4.0, atrial fibrillation of any grade, bypass graft in
             coronary/peripheral artery, symptomatic congestive cardiac failure, cerebrovascular
             accident including transient ischemic attack, or symptomatic pulmonary embolism.

         17. Known hypersensitivity to any PD 0332991 or excipients.

         18. Active or recent suicide attempt or behavior.