Patient-Derived Xenografts in Personalizing Treatment for Patients With Relapsed/Refractory Mantle Cell Lymphoma

Inclusion Criteria: * FOR TISSUE COLLECTION TO ESTABLISH PDX (PART 1): Confirmed MCL tissue diagnosis. * FOR TISSUE COLLECTION TO ESTABLISH PDX (PART 1): Patients must have relapsed/progressed after any therapy for MCL. * FOR TISSUE COLLECTION TO ESTABLISH PDX (PART 1): Understand and voluntarily sign an Institutional Review Board (IRB)-approved informed consent form. * FOR TISSUE COLLECTION TO ESTABLISH PDX (PART 1): Patients must be willing to allow residual tissue to be collected for both in vitro, in vivo (PDX) testing and molecular profiling. * FOR TISSUE COLLECTION TO ESTABLISH PDX (PART 1): Patients must have bi-dimensional measurable disease as per Lugano criteria (bone marrow or gastrointestinal \[GI\] only involvement is acceptable). * FOR TISSUE COLLECTION TO ESTABLISH PDX (PART 1): Eastern Cooperative Oncology Group (ECOG) performance status of 0-2. * FOR TISSUE COLLECTION TO ESTABLISH PDX (PART 1): Disease free of other prior malignancies of \>= 3 years with exception of currently treated basal cell, squamous cell carcinoma of the skin, carcinoma "in situ" of the cervix or breast, or other malignancies in remission (including prostate cancer patients in remission from radiation therapy, surgery or brachytherapy) or not actively being treated, with a life expectancy \> 2 years. * FOR TISSUE COLLECTION TO ESTABLISH PDX (PART 1): Reasonable expectation that the patient can wait 3-6 months for generation of PDX data for subsequent treatment selection. * FOR PDX-GUIDED THERAPY THROUGH ONGOING TRIALS AT MD ANDERSON OR OFF-PROTOCOL WITH STANDARD OF CARE (PART 2): The patient PDXs must have generated informative mouse xenograft data during Part 1 to participate in Part 2. * FOR PDX-GUIDED THERAPY THROUGH ONGOING TRIALS AT MD ANDERSON OR OFF-PROTOCOL WITH STANDARD OF CARE (PART 2): The patient condition remains suitable for the selected therapy. If the patient receives prior therapy with a given agent (X) and progressed, but the testing in Part 1 found this agent to be effective in a combination, the patient remains eligible for this combination that includes agent X. * FOR PDX-GUIDED THERAPY THROUGH ONGOING TRIALS AT MD ANDERSON OR OFF-PROTOCOL WITH STANDARD OF CARE (PART 2): Patients should ideally have bi-dimensional measurable disease (leukemia phase only, bone marrow only, splenomegaly only, or GI involvement only is acceptable). * FOR PDX-GUIDED THERAPY THROUGH ONGOING TRIALS AT MD ANDERSON OR OFF-PROTOCOL WITH STANDARD OF CARE (PART 2): Women of childbearing potential (WCBP) must have a negative serum or urine pregnancy test. Men must agree not to father a child and agree to use a condom if his partner is of child-bearing potential. * FOR PDX-GUIDED THERAPY THROUGH ONGOING TRIALS AT MD ANDERSON OR OFF-PROTOCOL WITH STANDARD OF CARE (PART 2): Patients must have adequate organ function for drugs(s) or combination being utilized (dependent on the drug\[s\] being given). Exclusion Criteria: * Any serious medical condition that places the patient at unacceptable risk and/or would prevent the subject from signing the informed consent form. Examples include but are not limited to uncontrolled hypertension, uncontrolled diabetes mellitus, active /symptomatic coronary artery disease, active infection, active hemorrhage, and psychiatric illness. * Pregnant or breastfeeding females. * 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). Known hepatitis C infection is allowed as long as there is no active disease and is cleared by GI consultation. * 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 with a life expectancy \< 2 years. * Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure or myocardial infarction within 6 months at the time of consent or any class 3 (moderate) or 4 (severe) cardiac disease defined by the New York Heart Association classification. * Prior chemotherapy within 3 weeks, nitrosoureas within 6 weeks, therapeutic anticancer antibodies within 4 weeks, radio- or toxin-immunoconjugates within 10 weeks, radiation therapy or other investigational agents within 3 weeks, major surgery within 4 weeks or vaccination with live attenuated vaccines within 4 weeks of the first dose of study drug. * THE PATIENT IS INELIGIBLE TO PARTICIPATE IN PART 2 IF ANY OF THE FOLLOWING OCCUR: PDX data are non-informative. * THE PATIENT IS INELIGIBLE TO PARTICIPATE IN PART 2 IF ANY OF THE FOLLOWING OCCUR: Tumors do not engraft in the mice or do not respond to any of the selected agents. * THE PATIENT IS INELIGIBLE TO PARTICIPATE IN PART 2 IF ANY OF THE FOLLOWING OCCUR: In Cohort 2, if disease progression occurs before Part 1 data are available, then they will be transferred to Cohort 1. * THE PATIENT IS INELIGIBLE TO PARTICIPATE IN PART 2 IF ANY OF THE FOLLOWING OCCUR: Part 1 data contradict clinical judgment. The investigator should discuss with the principal investigator (PI) and use the best discretion. * THE PATIENT IS INELIGIBLE TO PARTICIPATE IN PART 2 IF ANY OF THE FOLLOWING OCCUR: Any other exclusion criteria set forth by individual treatment protocol of the active clinical trial(s) through which patients are going to be treated.