Inclusion Criteria:

        Phase I: Patients must have histologically confirmed relapsed or refractory Non-Hodgkin's
        lymphoma, Hodgkin's Disease or multiple myeloma (defined by World Health Organization (WHO)
        criteria).

        Phase II: Patients must have histologically confirmed relapsed or refractory T-Cell
        Lymphoma (as defined by WHO criteria).

          -  Must have received first line chemotherapy. No upper limit for the number of prior
             therapies

          -  Evaluable Disease

          -  Age ≥18 years

          -  Eastern Cooperative Oncology Group (ECOG) performance status ≤2

          -  Patients must have adequate organ and marrow function as defined in the protocol

          -  Adequate Contraception

          -  Ability to understand and the willingness to sign a written informed consent document

          -  Inclusion Criteria for Multiple Myeloma patients specified in the protocol

        Exclusion Criteria:

          -  Prior Therapy

               -  Exposure to chemotherapy or radiotherapy within 2 weeks (6 weeks for nitrosureas
                  or mitomycin C) prior to entering the study or those who have not recovered from
                  adverse events due to agents administered more than 2 weeks earlier

               -  Systemic steroids that have not been stabilized to the equivalent of ≤10 mg/day
                  prednisone prior to the start of the study drugs

               -  No other investigational agents are allowed

          -  Central nervous system metastases, including lymphomatous meningitis

          -  History of allergic reactions to Pralatrexate or Romidepsin

          -  Uncontrolled intercurrent illness

          -  Pregnant women

          -  Nursing women

          -  Current malignancy or history of a prior malignancy, as outlined in the protocol

          -  Patient known to be Human Immunodeficiency Virus (HIV)-positive

          -  Active Hepatitis A, Hepatitis B, or Hepatitis C infection