Pembrolizumab and Pemetrexed for Progressive Chordoma

Inclusion Criteria: In order to be eligible to participate in this study, an individual must meet the criteria listed below. 1. Participant has the ability to understand and the willingness to provide a signed and dated informed consent form. 2. Participant has the willingness to comply with all study procedures and availability for the duration of the study. 3. Participant has a pathologic diagnosis of chordoma. 4. Evidence of progressive disease within the past six months before study entry, according to RECIST v1.1. 5. Participant has measurable disease, according to RECIST v1.1. 6. Participant is male or female, ≥ 18 years of age. 7. Participant has an Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 to 1 at study entry: ECOG Performance Status Grade Description 0 Normal activity. Fully active, able to carry on all pre-disease performance without restriction. 1. Symptoms, but ambulatory. Restricted in physically strenuous activity, but ambulatory and able to carry out work of a light or sedentary nature (e.g., light housework, office work). 2. In bed \<50% of the time. Ambulatory and capable of all self-care, but unable to carry out any work activities. Up and about more than 50% of waking hours. 3. In bed \>50% of the time. Capable of only limited self-care, confined to bed or chair more than 50% of waking hours.- 4. 100% bedridden. Completely disabled. Cannot carry on any self-care. Totally confined to bed or chair. 5. Dead. Note: Special allowance may be made for inclusion of participants with an ECOG PS of 2 if status is due to disease-related impingement of the spinal cord rather than other underlying comorbidities. 8\. Participant has adequate organ function: 1. ANC ≥ 1.5 x 109/L 2. Platelets ≥ 100 x 109/L 3. Hemoglobin ≥ 9 g/dL or ≥ 5.6 mmol/L Note: Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks. 4. Total bilirubin ≤ 1.5 x ULN Note: Patients with Gilbert's syndrome with a total bilirubin ≤ 2.0 ULN and direct bilirubin within normal limits are permitted. 5. ALT and AST ≤ 2.5 x ULN (≤ 5 x ULN in presence of known hepatic metastasis) 6. Serum creatinine ≤ 1.5 x ULN 9. Participant has the ability to interrupt non-steroidal anti-inflammatory drugs (NSAIDS) 2 days before (5 days for long-acting NSAIDs), the day of, and for 2 days following administration of Pemetrexed. 10\. Participant has the ability to take folic acid, Vitamin B12, and dexamethasone according to the protocol schedule. 11\. Participant has recovered from any previous therapy-related toxicity to CTCAE Grade 1 or to their clinical baseline at study entry. 12\. Criteria for known Hepatitis B and C positive participant: Hepatitis B screening tests are required. 12.1 Hepatitis B positive participants • Participants who are HBsAg positive are eligible if they have received HBV antiviral therapy for at least 4 weeks and have undetectable HBV viral load prior to study intervention. * Participants should remain on anti-viral therapy throughout study intervention and follow local guidelines for HBV anti-viral therapy post completion of study intervention. 12.2 Participants with history of HCV infection are eligible if HCV viral load is undetectable at screening. * Participants must have completed curative anti-viral therapy at least 4 weeks prior to study intervention 13. Male participant: agrees to use highly effective contraception as detailed in Section 4.3.2 of this protocol during the treatment period and for at least 120 days after the last dose of study intervention and refrain from donating sperm during this period. 14\. Female participant: meets at least one of the following conditions: a. Not a woman of childbearing potential (WOCBP) as defined in Section 4.3.2. OR b. Is a WOCBP who agrees to use highly effective contraception as detailed in Section 4.3.2 of this protocol during the study treatment period and for at least 120 days after the last dose of study intervention. Exclusion Criteria: 4.2 PARTICIPANT EXCLUSION CRITERIA An individual who meets any of the following appropriate criteria below will be excluded from participation in this study. 1. Participant has insufficient time from prior therapy to the first dose of study treatment: 1. Less than 4 weeks for an investigational agent or investigational device 2. Less than 3 weeks for major surgery 3. Less than 2 weeks for radiation therapy 4. Less than 3 weeks for a cytotoxic agent 5. Less than 2 weeks or 5 half-lives, whichever is shorter, for a targeted therapy (e.g. tyrosine kinase inhibitor) 6. Less than 3 weeks or 5 half-lives, whichever is shorter, for an antibody-based therapy 2. Participant has received a live vaccine or live-attenuated vaccine within 30 days before the first dose of study intervention. Note: Please refer to Section 6.4 for information on COVID-19 vaccines. 3. Participant has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study intervention. 4. Participant has active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). Note: Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. 5. Participant has an active bacterial infection requiring intravenous \[IV\] antibiotics at time of initiating study treatment, fungal infection, or detectable viral infection. 6. Participant has a known history of non-infectious pneumonitis or currently has pneumonitis. 7. Participant has a known history of human immunodeficiency virus (HIV) infection. 8. Partic