This research study is evaluating a drug called carfilzomib used in combination with another drug called belinostat with participants who have relapsed or refractory non-Hodgkin lymphoma (NHL).

The investigators are looking for the highest dose of the study drug that can be administered safely without severe or unmanageable side effects in participants that have NHL, not everyone who participates in this research study will receive the same dose of the study drug. The dose the each participant gets will depend on the number of participants who have been enrolled in the study prior and how the dose was tolerated.

• Study Drug(s): Both carfilzomib and belinostat will be given through a vein in the participant's arm (IV infusion). Each treatment cycle lasts 28 days (4 weeks).

  • Carfilzomib will be given on Days 1-2, 8-9, and 15-16 of each cycle. The carfilzomib infusion will be given over about 10 minutes during the first cycle. However if the dose is increased over the course of the trial, or if in one of the groups that joins the study at a higher dose level, the infusion will last about 30 minutes. All participants will remain at the clinic under observation for at least 1 hour following each dose of carfilzomib during Cycle 1 and after the Cycle 2 Day 1 dose.
  • Belinostat will be given on Days 1-5 of each cycle. The belinostat infusion will be given over about 30 minutes.

• Clinical Exams: During all cycles the participant will have a physical exam and will be asked questions about their general health and specific questions about any problems any medications you may be taking.

• Pharmacokinetic (PK) blood tests: One of the main reasons for this study is to find the highest dose of the study drug combination that can be used safely without experiencing severe side effects to use for future studies. Once this dose is found (the maximum tolerated dose, or MTD), additional blood samples will be drawn from a small set of participants (about 5 participants total) to learn more about the activity of the study drugs in the body over a period of time, including the ways the study drugs are absorbed, distributed, and then released from the body. If participating in this group (the participant will be informed from the Investigator) these pharmacokinetic (PK) samples will be drawn repeatedly over a period of 24 hours on certain days: Blood samples will be drawn at 0, 15, 30, 60, 90 minutes, and 2, 4, 6, 8 and 24 hours after the study drug dosing on Days 1-2, 4-5, and 9 of Cycle 1.

• Scans (or Imaging tests): Tumor assessment by CT or PET CT scans once every 8 weeks (every other cycle).

Inclusion Criteria:

• Subjects must have histologically confirmed relapsed or refractory non-Hodgkin lymphoma that is not a candidate for standard curative therapy. NHL subtypes include: Diffuse large B-cell lymphoma (DLBCL), Mantle cell lymphoma, Marginal zone lymphoma, Lymphoplasmacytic lymphoma, Peripheral T-cell lymphomas, and Follicular lymphoma of any grade.

• Patients must have received at least one prior systemic therapy for lymphoma. A washout period of at least 3 weeks is required from the most recent prior therapy.

• Age ≥18 years

• ECOG performance status ≤ 2 (Karnofsky ≥ 60%, see Appendix A)

• Participants must have organ and marrow function as defined below:

  • absolute neutrophil count ≥1,000/mcL

  • platelets ≥75,000/mcL

  • total bilirubin ≤ 2 × institutional upper limit of normal

  • AST(SGOT)/ALT(SGPT) ≤ 3 × institutional upper limit of normal

  • creatinine ≤1.5 × institutional upper limit of normal

    --- OR

  • creatinine clearance ≥45 mL/min/1.73 m2 for participants with creatinine levels above institutional normal.

• Participants may have either measurable or non-measurable disease, but in all cases eligible patients must have disease that can be clinically evaluated for improvement or progression.

• Patients must have fully recovered from major surgery and from the acute toxic effects of prior chemotherapy and radiotherapy (residual grade 1 toxicity, e.g., grade 1 peripheral neuropathy, and residual alopecia are allowed).

• The effects of carfilzomib and belinostat on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of study drug administration.

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

Exclusion Criteria:

• Participants who have had chemotherapy or radiotherapy within 3 weeks (8 weeks for radioimmunotherapy) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 3 weeks earlier.
• Participants who are receiving any other investigational agents.
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to carfilzomib or belinostat
• Patients with a systemic fungal, bacterial, viral, or other infection not controlled
• Pregnant or lactating patients.
• Prior history of another malignancy (except for non-melanoma skin cancer, in situ cervical or breast cancer, or prostate cancer detectable only by PSA) unless disease free for over one year
• Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
• Congestive heart failure of any severity (NYHA class I-IV)
• Any active angina or any unstable angina pectoris or myocardial infarction within one year of study entry.
• Left ventricular ejection fraction below the lower limit of normal
• Greater than grade 1 peripheral neuropathy at baseline
• Congenital long QT syndrome or history of torsades de pointes
• Baseline QTc interval > 500 msec
• Concomitant medications required on dosing days that increase risk of torsades de pointes
• Subjects with known HIV infection
• Active hepatitis B or C infection
• Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib)
• Contraindication to any of the required concomitant drugs or supportive treatments, including hypersensitivity to all anticoagulation and antiplatelet options, antiviral drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment
• Subjects with pleural effusions requiring thoracentesis or ascites requiring paracentesis within 14 days prior to randomization