Study of MK-3475 Alone or in Combination With Copanlisib in Relapsed or Refractory NK and T-cell Non-Hodgkin Lymphoma

Inclusion Criteria: 1. Have a histologically or cytologically confirmed relapsed/refractory mature T-cell lymphoma that has progressed after a minimum of 1 systemic therapy with any of the following T-cell histologies: * Peripheral T-cell NHL, not other wise specified (PTCL, NOS) * Anaplastic large cell T-cell lymphoma (ALCL) * Anaplastic lymphoma kinase positive or negative * Angioimmunoblastic T-cell lymphoma * Subcutaneous panniculitis like T-cell lymphoma * Follicular T-cell lymphoma * Nodal peripheral T-cell lymphoma with TFH phenotype * Monomorphic epitheliotropic intestinal T-cell lymphoma (MEITL) * Enteropathy associated T-cell lymphoma * Hepatosplenic T-cell lymphoma * Extranodal NK/T-cell lymphoma, nasal type * Unclassifiable PTCL * Transformed cutaneous T-cell lymphoma (CTCL) to PTCL with systemic involvement (not local skin transformation). 2. Be willing and able to sign written informed consent for the trial. 3. Be at least 18 years of age on day of signing informed consent. 4. Have measurable disease based as defined by at least one lesion that can be measured in least 2 perpendicular dimensions and measures at least 1.5 cm in its long axis. 5. Have provided tissue from an archival tissue sample or newly obtained core or excisional biopsy of a tumor lesion obtained within 28 days prior to study enrollment. 6. Have a performance status of 0, 1 or 2 on the ECOG Performance Scale. 7. Demonstrate adequate organ function as defined below, all screening labs should be performed within 10 days of treatment initiation. * Absolute neutrophil count (ANC) Greater than or equal to 1,500 /mcL, OR Greater than or equal to1,000 /mcL if lymphomatous bone marrow involvement Patients with documented marrow involvement may receive GCSF to achieve this value * Platelets greater than or equal to 100,000 / mcL, OR greater than or equal to 75,000 / mcL if lymphomatous bone marrow involvement Patients with documented marrow involvement may be transfused to this value. * Hemoglobin greater than or equal to 9 g/dL or greater than or equal to 5.6 mmol/L Patients with documented marrow involvement may be transfused to this value. * Serum creatinine OR Measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCl) less than or equal to1.5 X upper limit of normal (ULN) OR greater than or equal to 40 mL/min for subject with creatinine levels greater than 1.5 X institutional ULN * Serum total bilirubin less than 1.5 X ULN OR Direct bilirubin less than the ULN for subjects with total bilirubin levels greater than 1.5 ULN * AST (SGOT) and ALT (SGPT) less than or equal to 2.5 X ULN OR less than or equal to 5 X ULN for subjects with liver involvement by lymphoma * Lipase less than or equal to 1.5 X ULN * International Normalized Ratio (INR) or Prothrombin Time (PT) less than or equal to 1.5 X ULN unless subject is receiving anticoagulant therapy * Activated Partial Thromboplastin Time (aPTT) less than or equal to 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants 8. Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication (Reference Section 5.5.2). Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for greater than 1 year. 9. Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy. Exclusion Criteria: 1. Is currently participating in or has participated in a study of an investigational agent or using an investigational device within 2 weeks of the first dose of treatment. 2. Patients diagnosed with Adult T-cell Leukemia/Lymphoma (ATLL) or T-cell PLL 3. Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. 4. Has had a prior monoclonal antibody within 4 weeks prior to study Day 1 or who has not recovered (i.e., worse than Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier. 5. Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent. * Note: Subjects with worse than Grade 2 neuropathy are an exception to this criterion and may qualify for the study. * Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. 6. Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy. 7. Has known active intraparenchymal lymphomatous central nervous system (CNS) lesions and/or lymphomatous meningitis. Subjects with previously treated CNS involvement by lymphoma 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 lesions, and are not using steroids for at least 7 days prior to trial treatment. 8. Has an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents. Subjects with vitiligo or resolved childhood asthma/atopy would be an exception to this rule. Subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study. Subjects with hypothyroidism stable on hormone replacement or Sjoegren's syndrome will not be excluded from the study. 9. Has evidence of interstitial lung disease or active, non-infectious pneumonitis. 10. Has an active infection requiring systemic therapy. 11. 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. 12. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 13. 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. 14. Has received prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-Cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways). 15. Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). 16. Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). 17. Has received a live vaccine within 30 days prior to the first dose of trial treatment. 18. Cohort 2a: Has received an allogeneic stem cell transplant. For cohort 2b, patients within the first 100 days of having undergone an allogeneic stem cell transplant will be excluded. Otherwise, patients who have received an allogeneic stem cell transplant are allowed as long as they have no evidence of active GVHD or are on immunosuppressive therapy 19. Uncontrolled arterial hypertension despite optimal medical management 20. Uncontrolled Type I or II diabetes mellitus as deemed appropriate by the investigator. Suggested guidelines for uncontrolled diabetes: HbA1c\> 8.5% 21. Anti-arrhythmic therapy (beta blockers or digoxin are permitted) 22. Use of CYP3A4 inhibitors and inducers. Copanlisib is primarily metabolized by CYP3A4. Therefore concomitant use of strong inhibitors of CYP3A4 (e.g., ketoconazole, itraconazole, clarithromycin, ritonavir, indinavir, nelfinavir and saquinavir), and strong inducers of CYP3A (e.g. rifampin, phenytoin, carbamazepine, phenobarbital, St. John's Wort) are not permitted from Day -14 of Cycle 1 until the Safety follow up visit. See Table in Appendix 5 for complete list 23. Concurrent diagnosis of pheochromocytoma 24. Arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism within 3 months before the start of study medication 25. Prior exposure to PI3K inhibitors, unless on PI3K inhibitor therapy more than 6 months ago AND reason for discontinuation of prior PI3K inhibitor therapy was other than progression or toxicity. 26. Patients with detectable CMV viremia are excluded