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

• ECOG 0-1 at enrollment.

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

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

• 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);

• 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.

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

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

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

⁃ Measurable disease according to RECIST 1.1 criteria.

⁃ 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.

• Mutation of CDKN2A gen.

• ECOG 0-1 at the time of inclusion.

• Centrally confirmed diagnosis of chordoma (metastatic or locally advanced inoperable).

• Disease progression according to RECIST 1.1, within the year prior to inclusion, to previous treatment (surgery, radiotherapy or systemic treatment).

• Patients are not candidates for salvage surgery or radiotherapy at the time of inclusion.

• Patients must have the following lab results:

‣ Absolute neutrophil count ≥ 1,500/mm3 (1.5 x 109/L);

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

⁃ Hemoglobin ≥ 9 g/dL (90 g/L);

⁃ Blood creatinine ≤ 1.5 x ULN or estimated creatinine clearance ≥ 60 mL/min;

⁃ Total blood 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 there is liver metastasis);

⁃ Alkaline phosphatase ≤ 2.5 x ULN (≤ 5.0 x ULN if there is bone or liver metastasis);

• The patients must have signed the written consent to participate in the clinical study, and to provide the tumor blocks in paraffin for the molecular analysis of the screening phase.

• Biopsy at baseline if there are no archive tumor samples obtained in the 3 months prior to starting treatment. If there are tumor samples within this period, there should not be subsequent treatments.

• Patients may have received up to 3 previous lines of systemic treatment.

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

⁃ Measurable disease according to RECIST 1.1 criteria.

⁃ All patients (male and female) of childbearing potential must use effective contraception throughout treatment with palbociclib and for at least 90 days after the last dose. Pregnancy must be ruled out by urine or blood test (negative pregnancy test) for inclusion in the study. Men should be told to consider sperm preservation before starting treatment due to the risks of infertility.