Ixazomib & Rituximab After Stem Cell Transplant in Treating Patients With Mantle Cell Lymphoma in Remission

Inclusion Criteria: * Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care. * Female patients who: * Are postmenopausal for at least 1 year before the screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential, agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject; (periodic abstinence \[eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception). * Male patients, even if surgically sterilized (ie, status post-vasectomy), must agree to one of the following: * Agree to practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject; (periodic abstinence (eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception). * Patients must have a diagnosis of mantle cell lymphoma confirmed at diagnosis by one of the following: * t(11;14) detected by fluorescence in situ hybridization (FISH), conventional cytogenetics, or other molecular evaluation * Expression of cyclin D1 confirmed by immunohistochemistry. * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2. * Patients must have completed an autologous stem cell transplant after their first course of treatment; patients who have relapsed or progressed at any time prior to transplant are not eligible. * Patients must not have experienced confirmed progressive disease since the time of their transplant. * Absolute neutrophil count (ANC) ≥ 1,000/mm³ and platelet count ≥ 75,000/mm³. Platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment. Patients may receive growth factor support prior to initiating therapy but must remain off of growth factor for at least 7 days before starting therapy and must meet eligibility on cycle 1, day 1. Patients who complete the consent process but do not meet hematologic eligibility within 30 days may be re-consented and enrolled on study if they ultimately do meet eligibility requirements before day +180. No patients may initiate therapy after day +180 and they must meet all remaining eligibility criteria. * Total bilirubin ≤ 1.5 x the upper limit of the normal range (ULN) except for previously documented Gilbert's disease, defined as a mild unconjugated hyperbilirubinemia with no other identifiable cause and bilirubin values \< 6 mg/dL; patients with hyperbilirubinemia secondary to presumed Gilbert's disease who are being considered for enrollment in the study MUST have a fractionated bilirubin included in their screening labs when determining eligibility. * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3 x ULN. * Calculated creatinine clearance ≥ 30 mL/min using Cockcroft-Gault formula. * Note: Patients are expected to initiate therapy as close to day +100 as possible. No patient may initiate therapy before day +70 and initiation of therapy beyond day +130 is allowed ONLY for patients who meet all eligibility criteria except for hematologic parameters, in which case patients may be delayed until their hematologic laboratories meet criteria but no later than day +180. Regardless of the time of therapy initiation, patients must meet all eligibility criteria and must have completed all consent documentation and screening procedures within the specified window. Exclusion Criteria: * Female patients who are lactating or have a positive serum pregnancy test during the screening period. * Failure to have fully recovered (ie, ≤ grade 1 toxicity) from the reversible effects of prior chemotherapy, except for laboratory abnormalities which are addressed above. * Major surgery within 14 days before enrollment. * Radiotherapy within 14 days before enrollment; if the involved field is small, 7 days will be considered a sufficient interval between treatment and administration of the ixazomib. * Central nervous system involvement with lymphoma at any time in the patient's history; intrathecal prophylaxis during induction is allowed as long as active disease has not been identified. * Infection requiring intravenous antibiotic therapy or other serious infection within 14 days before study enrollment. * Evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, uncontrolled cardiac arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial infarction within the past 6 months; patients experiencing an isolated cardiac complication at the time of transplant who have been evaluated by cardiology and remained stable for at least 60 days are eligible. * Systemic treatment, within 14 days before the first dose of ixazomib, with strong cytochrome P450, family 3, subfamily A (CYP3A) inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or use of St. John's wort. * Ongoing or active systemic infection, active hepatitis B or C virus infection, or known human immunodeficiency virus (HIV) positive. Patients who have previously tested positive for hepatitis B core antibody may be eligible if they are confirmed to NOT have active disease and are on appropriate anti-viral therapy. No additional hepatitis or HIV testing is required for patients who have been evaluated during their induction and/or pre-transplant work-up and have had no clinical evidence of HIV, hepatitis B or hepatitis C since their last evaluation. * Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol. * Known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent. Patients with a prior reaction to rituximab are permitted if the investigator feels that this reaction is manageable with standard supportive care measures and would otherwise be comfortable administering rituximab outside of the clinical trial setting. * Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of ixazomib including difficulty swallowing; patients with known GI involvement with mantle cell lymphoma who have no clinical evidence of active disease at the time of enrollment are eligible. * Diagnosed or treated for another malignancy within 2 years before study enrollment or previously diagnosed with another malignancy and have any evidence of residual disease; patients with non-melanoma skin cancer, carcinoma in situ of any type, or low risk cervical cancer are not excluded if they have undergone complete resection and are deemed free of disease by their treating physician; patients with low risk prostate cancer who are under observation are eligible if their urologist or oncologist does not expect them to require therapy within 1 year. * Patient has ≥ grade 3 peripheral neuropathy, or grade 2 with pain on clinical examination during the screening period. * Receipt of therapy on a clinical trial, including investigational and non-investigational agents not included in this trial, within 30 days of the start of this trial and throughout the duration of this trial; participation on non-therapeutic clinical studies is allowed, and patients who participated on a clinical trial for induction and/or transplant but who have completed the prescribed therapy course for that study and have been off therapy for at least 30 days are eligible. * Prior exposure to ixazomib; however, prior bortezomib exposure is allowed. * Patients with any history of relapsed/refractory disease, or who have progressed at any time since beginning induction therapy are not eligible; patients who have evidence of residual disease by FISH, cytogenetics, SNP array, or flow cytometry without any measurable nodal disease or morphologic evidence of disease in the bone marrow or peripheral blood are eligible.