Trial of PCI-32765 (BTK Inhibitor) in Combination With Carfilzomib in Relapse/Refractory Mantle Cell Lymphoma

Inclusion Criteria:

1. Patients must have a confirmed diagnosis of mantle cell lymphoma with positivity in tissue biopsy.
2. Patients must have previously treated relapsed and/or refractory MCL with at least 2 prior lines of therapy (prior carfilzomib, ibrutinib, bortezomib, anthracycline, rituximab or stem cell transplant are acceptable). There is no upper limit for prior lines of therapy.
3. Understand and voluntarily sign an institutional review board (IRB)-approved informed consent form.
4. Age \>/= 18 years at the time of signing the informed consent.
5. Patients must have bi-dimensional measurable disease (Measureable disease by CT scan defined as at least 1 lesion that measures =/\>1.5 cm in single dimension.) Patient with leukemia phase (peripheral blood involvement), non-measurable disease, gastrointestinal (GI) MCL, or bone marrow (BM) MCL are also eligible.
6. Gastrointestinal or bone marrow or spleen only patients are allowable and will be analyzed separately.
7. Eastern Cooperative Oncology Group (ECOG) performance status of 2 or less
8. Serum bilirubin \<1.5 mg/dl and creatinine (Cr) Clearance \>/= 30 mL/min, platelet count \>75,000/mm\^3 and absolute neutrophil count (ANC) \> 1,500/mm\^3, aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) and alanine aminotransferase (ALT)/serum glutamic pyruvic transaminase (SGPT) \< 3 x upper limit of normal or \< 5 x upper limit of normal if hepatic metastases are present. (Patients who have bone marrow infiltration by MCL are eligible if their ANC is \>/= 1000/mm\^3 \[growth factor not allowed\] or their platelet level is \>/= 50,000/mm\^3).
9. Willing and able to participate in all study related procedures and therapy including swallowing capsules without difficulty.
10. Females of childbearing potential (FCBP)\* must have a negative serum or urine pregnancy test and must be willing to use acceptable methods of birth control during the study and for 30 days after the last dose of study treatment. \* A female of childbearing potential is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) 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).
11. Male patients must use an effective barrier method of contraception during the study and for 30 days following the last dose of study treatment if sexually active with a female of childbearing potential.

Exclusion Criteria:

1. Any serious medical condition including but not limited to, uncontrolled hypertension, uncontrolled diabetes mellitus, uncontrolled infection, active/symptomatic coronary artery disease, chronic obstructive pulmonary disease (COPD), renal failure, active hemorrhage, or psychiatric illness that, in the investigators opinion places the patient at unacceptable risk and would prevent the subject from signing the informed consent form.
2. Pregnant or breastfeeding females.
3. Use of any standard/experimental anti-lymphoma drug therapy, including steroids, within 3 weeks of initiation of the study or use of any experimental non-drug therapy (e.g., donor leukocyte/mononuclear cell infusions) within 56 days of initiation of the study drug treatment.
4. Prior allogeneic stem cell transplant (SCT) within 16 weeks or autologous SCT within 8 weeks of initiation of therapy. (Patients that require immunosuppressive therapy are not eligible within 60 days of therapy.)
5. Known human immunodeficiency virus (HIV) infection. Patients with active Hepatitis B infection (not including patients with prior Hepatitis B vaccination; or positive serum Hepatitis B antibody). Hepatitis C infection is allowed as long as there is no active disease and is cleared by GI consultation.
6. All patients with central nervous system lymphoma.
7. Significant neuropathy (Grades 3-4, or Grade 2 with pain) within 14 days prior to enrollment.
8. Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib).
9. Contraindication to any of the required concomitant drugs or supportive treatments or intolerance to hydration due to preexisting pulmonary or cardiac impairment including pleural effusion requiring thoracentesis or ascites requiring paracentesis.
10. Malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel or ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction, or any other gastrointestinal condition that could interfere with the absorption and metabolism of ibrutinib.
11. Major surgery within 4 weeks of initiation of therapy.
12. Requires anticoagulation with warfarin or equivalent vitamin K antagonist.
13. Requires treatment with strong CYP3A inhibitors.
14. The patient has a prior or concurrent malignancy that in the opinion of the investigator, presents a greater risk to the patient's health and survival, than of the MCL, within the subsequent 6 months at the time of consent. Investigator discretion is allowed.
15. Patients with New York Heart Association (NYHA) Class III and IV heart failure, myocardial infarction in the preceding 6 months, and significant conduction abnormalities, including but not limited to atrial fibrillation, 2nd degree AV block type II, 3rd degree block, Torsade de pointe, QT prolongation (QTc \> 450 msec, sick sinus syndrome, ventricular tachycardia, symptomatic bradycardia (heart rate \< 50 bpm), hypotension, light headedness and syncope. Patients with atrial fibrillation will be excluded even if they are rate-controlled. If there are any active cardiac issues, cardiology consultation will be obtained for clearance.
16. Known history of Pulmonary Hypertension
17. If the left ventricular ejection fraction (LVEF) \< 40, patients will be excluded.
18. Known history of Cardiomyopathy
19. Acute infection requiring treatment (systemic antibiotics, antivirals, or antifungals) within 14 days prior to initiation of study.