Trial of Duvelisib in Combination With Either Romidepsin or Bortezomib in Relapsed/Refractory T-cell Lymphomas

Inclusion Criteria: * Pathologically confirmed T-cell lymphomas at the enrolling institution, including stage ≥ Ib CTCL, which has relapsed or progressed after at least one systemic therapy. * Age ≥ 18 * Previous systemic anti-cancer therapy must have been discontinued at least 3 weeks prior to treatment. For the dose expansion phase, in progressing subjects, a 2 week washout may be allowed after discussion with the MSK Principal Investigator. * Previous radiation and/or surgery must have been discontinued or completed at least 2 weeks prior to treatment in this study and adverse effects must have resolved to Grade 1 or baseline. Lymph node or other diagnostic biopsies within 2 weeks are not considered exclusionary. ° Patients who have received localized RT as part of their immediate prior therapy may be allowed to enroll with shorter washout period after discussion with the MSK Principal Investigator. * ECOG ≤ 2 * Meet the following laboratory criteria without use of growth factor support or platelet transfusions for 1 week: i) Absolute neutrophil count ≥ 1.0 K/mcl, ii) Platelet count ≥ 80 K/μl (in the expansion cohorts, if thrombocytopenia is due to bone marrow involvement platelet count must be ≥ 50 K/μL), iii) Patients enrolled in the dose escalation phase who are not enrolled on the expansion cohorts must have calculated creatinine clearance ≥ 50ml/min by Cockcroft-Gault formula. Patients enrolled in the Dose Expansion phase must have calculated creatinine clearance ≥ 40ml/min by Cockcroft-Gault formula. iv) Total bilirubin ≤ 1.5 x upper limit of normal (ULN) or ≤ 3 x ULN if documented hepatic involvement with lymphoma, or ≤ 5 x ULN if history of Gilbert's syndrome; AST (SGOT) and ALT (SGPT) ≤ 3 x ULN; ≤ 5 ULN if due to lymphoma involvement * Measurable disease for dose expansion and lead in phase only. Measurable disease defined by: 1. Revised International Working Group (Cheson, 2007) Classification for systemic lymphoma or 2. Atypical and or malignant lymphocytes quantifiable by flow cytometry or morphology in blood 3. or bone marrow mSWAT \> 0 or Sezary couny \>/= 1000 cells/ul * Short course systemic corticosteroids for disease control, improvement of performance status or non-cancer indication (\< 7 days) must have been discontinued at least 6 days prior to study treatment. Stable ongoing corticosteroid use (≥ 30 days) up to an equivalent dose of 20 mg of prednisone is permissible. i) Topical steroids that have been used for \> 3 weeks may be continued (CTCL only). All other histologies (not CTCL): Topical steroids use is permissible without restriction * Women of reproductive potential† must have a negative serum or urine β human chorionic gonadotropin (βhCG) pregnancy test. All women of reproductive potential, all sexually active male patients, and all partners of patients must agree to use adequate methods of birth control (e.g. latex condoms) throughout the study and for 30 days after the last dose of study drug. * A female of reproductive potential is a sexually mature female who: has not undergone a hysterectomy or bilateral oophorectomy; or has not been naturally postmenopausal for at least 24 consecutive months (i.e. has had menses at any time in the preceding 24 consecutive months). Exclusion Criteria: * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form. * Pregnant females. (Lactating females must agree not to breast feed while taking the study medications). * Prior use of duvelisib if discontinued due to toxicity. * For the romidepsin arm of the study, prior therapy with romidepsin if discontinued due to toxicity. * For the bortezomib arm of the study, prior therapy with a proteasome inhibitor if discontinued due to toxicity. * For the bortezomib arm of the study, patients with grade ≥2 peripheral neuropathy. * History of chronic liver disease, veno-occlusive disease, or current alcohol abuse. * Administration of a live vaccine within 6 weeks of first dose of study drug. * Prior surgery or gastrointestinal dysfunction that may affect drug absorption (e.g., gastric bypass surgery, gastrectomy) * Known seropositive and requiring anti-viral therapy for human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV). Subjects with chronic hepatitis B or C as defined as test . * Subjects with positive Hep B serology. Subjects with a negative HBsAg and a positive HBcAb require an undetectable/negative hepatitis B DNA test (e.g., polymerase chain reaction \[PCR\] test) to be enrolled, and will require prophylactic antiviral treatment (e.g., F) initiated prior to the first dose of study drug, an continued until approximately 6 to 12 months after completion of study drug(s). * Patients with positive hepatitis C virus Ab * Subjects with active EBV unrelated to underlying lymphoma (positive serology for anti-EBV VCA IgM antibody and negative for anti-EBV EBNA IgG antibody, or clinical manifestations and positive EBV PCR consistent with active EBV infection. * Subject with active CMV (positive serology for anti-CMV IgM antibody and negative for anti-CMV IgG antibody and positive CMV PCR with clinical manifestations consistent with active CMV infection) and requiring therapy will be excluded from participation in the study. Carriers will be monitored per institutional guidelines. * Receiving systemic therapy for another primary malignancy (other than T-cell lymphoma) * Patients with more than one type of lymphoma may be enrolled after discussion with the MSK Principal Investigator. * Adjuvant or maintenance therapy to reduce the risk of recurrence of other malignancy (other than T-call lymphoma) is permissible after discussion with the MSK Principal Investigator. * Known central nervous system or meningeal involvement (in the absence of symptoms, investigation into central nervous system involvement is not required). * Uncontrolled infection requiring systemic antimicrobials * The following known cardiac abnormalities: 1. Congenital long QT syndrome. 2. QTc/QTf interval ≥ 480 milliseconds; unless secondary to pacemaker or bundle branch block. 3. Myocardial infarction within 6 months. (Subjects with a history of myocardial infarction within the last 6 to12 months who are asymptomatic and have had a negative cardiac risk assessment (treadmill stress test, nuclear medicine stress test, or stress echocardiogram) since the event may participate.) 4. Other significant ECG abnormalities including 2nd degree atrio- ventricular (AV) block (AV) block type II, 3rd degree AV block. 5. Symptomatic coronary artery disease (CAD), e.g., angina Canadian Class II-IV (see Appendix B). In any patient in whom there is doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present. II-IV (see Appendix B). In any patient in whom there is doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present. 6. An ECG recorded at screening showing evidence of cardiac ischemia (ST depression of ≥2 mm, measured from isoelectric line to the ST segment). If in any doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present. 7. Congestive heart failure (CHF) that meets New York Heart Association (NYHA) Class II to IV definitions (see Appendix C) and/or ejection fraction \<45% by MUGA, echocardiogram, or cardiac MRI. 8. A known history of sustained ventricular tachycardia (VT), ventricular fibrillation (VF), Torsade de Pointes, or cardiac arrest unless currently addressed with an automatic implantable cardioverter defibrillator (AICD). 9. Hypertrophic cardiomegaly or restrictive cardiomyopathy from prior treatment or other causes. 10. Uncontrolled hypertension, i.e., blood pressure (BP) of ≥170/95; patients who have a history of hypertension controlled by medication must be on a stable dose (for at least one month prior to study registration) and meet all other inclusion criteria. 11. Any cardiac arrhythmia requiring an anti-arrhythmic medication (excluding stable doses of beta-blockers) 12. For patients enrolling on the Romidepsin arm; taking drugs associated with significant QTc/QTf prolongation, unless able to be switched to non-QTc/QTf prolonging medication or on a stable dose without significant QT prolongation (\>470 msec). Caution should be used when administering study drugs to patients taking medications significantly metabolized by these enzymes refer to (http://medicine.iupui.edu/clinpharm/ddis/clinical-table/) for clinically relevant medications. Particular attention should be paid to patients receiving warfarin. Patient should have coagulation parameters monitored regularly, and warfarin dose adjusted accordingly. If these drugs cannot be discontinued or replaced enrollment may be allowed after discussion with MSK PI.