This is an international, multicenter, multi-arm, phase Ib, model-based dose-escalation study. The primary objectives of the study in each arm is to determine the maximum tolerated dose (MTD), recommended phase 2 dose (RP2D), dose limiting toxicities (DLTs) and to evaluate the clinical efficacy at the MTD of various combinations of pembrolizumab, pralatrexate and decitabine.

The peripheral T-cell lymphomas (PTCLs) are rare subtypes of Non-Hodgkin lymphoma (NHL) with unique clinicopathologic features and very unfavorable prognosis. Recently it has been demonstrated that PTCLs are characterized by recurrent mutations in epigenetic operators (e.g. TET2, DNMT3A, and IDH2) and escape from immune surveillance.

The safety and toxicity of these combinations will be evaluated throughout the entire study. Dose allocation in Arms A and C will be based upon a continual reassessment method (CRM), and combination allocation in Arm B will be conducted using a DLT-adapted partial order continual reassessment method (POCRM) for dose-finding with combinations of agents.

Study Hypothesis: If pralatrexate and/or decitabine functions in an immunomodulatory fashion then priming and modulating the malignant cells and the microenvironment will enhance the antitumor activity of pembrolizumab in patients with PTCLs and CTCLs.

Inclusion Criteria:

1. Be willing and able to provide written informed consent/assent for the trial.
2. Be ≥ 18 years of age on day of signing informed consent.
3. Have measurable disease as defined by the Lugano Criteria for PTCL and by the Global Response Score for CTCL.
4. Patient must have histologically confirmed relapsed or refractory Peripheral T-cell lymphoma (PTCL) or cutaneous T-cell Lymphoma (CTCL) as per WHO criteria and TNMB classification and staging.
5. There is no upper limit for the number of prior therapies. Patient may have relapsed after prior autologous stem cell transplant.
6. Patients who had prior treatment for their disease, as long as there is radiographic evidence of refractory or relapsed disease and the patient meets all other clinical and laboratory criteria for study treatment.
7. Be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion. Be willing to provide FNA of a tumor lesion. Newly-obtained is defined as a specimen obtained up to 6 weeks (42 days) prior to initiation of treatment on Day 1. Subjects for whom newly obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived specimen only upon agreement from the Sponsor.
8. Have a performance status of 0 or 1 on the ECOG Performance Scale.
9. Demonstrate adequate organ function as defined in the protocol, all screening labs should be performed within 10 days of treatment initiation.
10. Female subjects of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required.
11. Female subjects of childbearing potential (Section 7.7.9.2) must be willing to use an adequate method of contraception as outlined in Section 7.9.2 - Contraception for the course of the study through 120 days after the last dose of study medication.
12. Male subjects of childbearing potential (Section 7.9.2) must agree to use an adequate method of contraception as outlined in Section 7.9.2- Contraception, starting with the first dose of study therapy through 120 days after the last dose of study therapy.

Exclusion Criteria:

1. Has lack of resolution of adverse events (AE) due to previously administered antineoplastic therapy to grade 1 or less according to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), version 5.0.
2. Had prior therapy with PD-1 inhibitors.
3. Has a diagnosis of immunodeficiency or has been receiving any immunosuppressive therapy within 7 days prior to the first dose of trial treatment. Use of steroid equivalent to prednisone 10 mg/day does not constitute an exclusion criterion.
4. Has a known history of active TB (Bacillus Tuberculosis)
5. Hypersensitivity to pralatrexate, or decitabine or pembrolizumab or any of its excipients.
6. Has received prior allogeneic stem cell transplant.
7. Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer.
8. Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability.
9. 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). 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. The following are exceptions to this criterion: subjects with vitiligo or alopecia; subjects with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement; subjects with psoriasis not requiring systemic treatment; patients with autoimmune phenomena secondary to active lymphoma.
10. Has known history of, or any evidence of non-infectious pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease.
11. Has an active infection requiring systemic therapy.
12. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator.
13. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
14. Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment.
15. Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent.
16. Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies).
17. Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA [qualitative] is detected).
18. Has received a live vaccine or live-attenuated vaccine within 30 days of planned start of study therapy. Administration of killed vaccines is allowed.

Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed