Primary Objective:

1. To determine objective response rate (ORR) according to RECIST v1.1 of pembrolizumab and high-dose pemetrexed in the treatment of patients with chordoma until disease progression. The OOR will be investigator assessed.

Secondary Objectives:

1. To describe the adverse events associated with administering pembrolizumab and high-dose pemetrexed combination treatment.
2. To determine disease control rate based on imaging and overall survival.
3. To determine median PFS and PFS rates at 6, 9, 12, and 18 months.
4. To evaluate changes in volumetric tumor measurements based on imaging.
5. To determine the effects of combination treatment on quality of life, assessed by the EORTC-QLQ-C30 questionnaire.
6. To assess tumor evolution over time in patients with chordoma based on imaging, and molecular profiling.
7. To assess the pharmacodynamic effects of treatment in blood.

Exploratory Objective:

1. To explore the relationship between molecular phenotype and patient response.

This purpose of this study is to test the effectiveness and safety of the research study drug combination of pembrolizumab and high-dose pemetrexed. Both drugs are approved by the U.S. Food and Drug Administration (FDA) for many different types of cancer but is considered investigational because it is not approved by the FDA for use in patients with a rare type of cancer called chordoma. Pembrolizumab (Keytruda) is approved for use in more than ten types of cancer. Pemetrexed (Alimta) is approved for use in patients with certain types of lung cancer called non-squamous non-small cell lung cancer (NSCLC) and malignant pleural mesothelioma. Pemetrexed is also approved for use with pembrolizumab and cisplatin or carboplatin for certain non-squamous NSCLC. The approved dose of pemetrexed is 500 mg/m2, but this study is evaluating a higher dose (900 mg/m2) in effort to deliver more drug to chordoma. Outcome measures will be monitored until disease progression, through study completion (estimated average of 2 years), or withdrawal from study.

Chordoma tumors can occur anywhere along the spine, from the head to the tailbone, and surgery and radiation therapy are currently used as treatment for chordoma. There are no drugs at this time that are approved for treating this cancer type. This study is being done to determine how the combination treatment regimen of pembrolizumab and high-dose pemetrexed might affect the growth of chordoma and to learn more about this regimen's safety in patients with 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. Participant has concurrent active Hepatitis B (defined as HBsAg positive and/or detectable HBV DNA) or Hepatitis C virus (defined as anti-HCV Ab positive and detectable HCV RNA) infection.

   Note: Hepatitis C screening is not required unless the participant has a known history of HCV infection.

9. Participant has had an allogenic tissue/solid organ transplant.

10. Participant has third space fluid which cannot be controlled by drainage. Note: For patients who develop or have baseline clinically significant pleural or peritoneal effusions (on the basis of symptoms or clinical examination) before or during initiation of pemetrexed therapy, consideration should be given to draining the effusion prior to dosing. However, if, in the investigator's opinion, the effusion represents progression of disease, the patient should be discontinued from study therapy.

11. Participant has a severe or uncontrolled medical disorder that would, in the investigator's opinion, impair ability to receive study intervention, including, but not limited to:

    1. Uncontrolled diabetes;
    2. Renal disease that requires dialysis;
    3. Pulmonary disorder requiring supplemental oxygen to keep saturation >95% and the situation is not expected to resolve within 2 weeks;
    4. Severe dyspnea at rest or requiring oxygen therapy;
    5. Interstitial lung disease;
    6. History of major surgical resection involving the stomach or small bowel;
    7. Preexisting Crohn's disease;
    8. Ulcerative colitis;
    9. Uncontrolled vasculitis and/or disease with known vasculitis;
    10. Preexisting chronic condition resulting in baseline Grade 2 or higher diarrhea;
    11. Psychiatric illness, substance abuse, or other social situation that would interfere with cooperation with the requirements of the trial.

12. Participant has a personal history or presence of any of the following cardiovascular conditions:

    1. Syncope of cardiovascular etiology;
    2. Ventricular arrhythmia of pathological origin (including, but not limited to, ventricular tachycardia and ventricular fibrillation);
    3. Myocardial infraction within 6 months of investigational product administration;
    4. Unstable angina;
    5. Sudden cardiac arrest;
    6. Congestive heart failure (NYHA classification ≥ 3):

    New York Heart Association Functional Classification Class Patient Symptoms I No limitation of physical activity. Ordinary physical activity does not cause undue fatigue, palpitation, dyspnea (shortness of breath).

    II Slight limitation of physical activity. Comfortable at rest. Ordinary physical activity results in fatigue, palpitation, dyspnea (shortness of breath).

    III Marked limitation of physical activity. Comfortable at rest. Less than ordinary activity causes fatigue, palpitation, or dyspnea.

    IV Unable to carry on any physical activity without discomfort. Symptoms of heart failure at rest. If any physical activity is undertaken, discomfort increases.

13. Participant has a known additional malignancy that is progressing or has required active treatment with the past 3 years.

    Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, organ confined prostate cancer, or carcinoma in situ, excluding carcinoma in situ of the bladder, that have undergone potentially curative therapy are not excluded.

14. Participant is a woman of childbearing potential (WOCBP) who is pregnant or nursing.

    Note: WOCBP should only be included after a negative highly sensitive urine or serum pregnancy test.

15. Participant has a history of severe hypersensitivity (≥ Grade 3) to pembrolizumab and/or any of its excipients (L-histidine, polysorbate 80, or sucrose).