Patients may have received one or more lines of prior chemotherapy with/without rituximab (including high dose therapy plus stem cell transplant which is counted as one regimen); prior bortezomib is allowed; patients must not have received bortezomib in the past 6 months Patients with clear cell or neuroendocrine cell types Stem Cell Transplant (SCT): * Patients are eligible 6 weeks after date of autologous stem cell infusion following myeloablative therapy (timed from first day of protocol therapy)* Patients are not eligible post allogeneic stem cell transplant* Patients who have received an autologous stem cell infusion to support non-myeloablative therapy (such as 131 iodine [I]-MIBG) are eligible at any time as long as they meet the other criteria for eligibility STEP II: Patients must not have received any non-protocol therapy outside of the assigned induction therapy including stem cell transplant Patients are eligible >= 6 weeks after autologous stem cell transplants or stem cell infusions as long as hematologic and other eligibility criteria have been met ONCOLOGY PATIENTS: patients with an oncology diagnosis that are or will be on a chemotherapy regimen that will last for an additional >= 3 months or are on or will be on a chemotherapy regimen for < 3 months and then proceed to transplant (allogeneic or autologous stem cell rescue) during the 3-month study period Must have undergone allogeneic hematopoietic stem cell transplantation (HSCT) (regardless of stem cell source) Stem cell Infusion without TBI: no evidence of active graft vs host disease and at least 84 days must have elapsed after transplant or stem cell infusion Stem cell transplant or rescue: patient has not had a prior stem cell transplant or rescue Patients who have received any of the following:* > 2 chemotherapy regimens* Myeloablative chemotherapy with stem cell rescue* Craniospinal irradiation Patients must not be candidates for allogeneic hematopoietic stem cell transplant; NOTE: Subjects up to age 70 years who are considered fit for allogeneic hematopoietic stem cell transplant, should be considered for enrollment on E1910, in order to avoid competing with that study; if a patient is considered unfit for intensive chemotherapy at the time of initial diagnosis, but subsequently achieves a complete remission (CR), then it will be left to the treating physicians discretion to consider hematopoietic stem cell transplant (HSCT) No prior treatment with high-dose chemotherapy (defined as treatment utilizing stem cell rescue) Patient is not a candidate for stem cell transplant due to advanced age or co-morbidities; or the enrollee does not have donor available; or the enrollee declines stem cell transplant due to personal belief; or stem cell transplant is not standard of care based on the risk category of disease Patients with chronic GVHD diagnosed within 3 years after hematopoietic stem cell transplant (HSCT) for any disease, with any graft, and any conditioning regimen with at least one manifestation secondary to fibrosis, including: sclerodermatous skin changes, dry mouth, dry eye, esophageal strictures, or vaginal GVHD Patient must be >= 12 weeks since autologous bone marrow/stem cell transplant prior to enrollment Stem cell transplant within previous 3 months prior to initiation of study therapy Current candidacy for a potentially curative allogeneic stem cell transplant, unless declined Patient must be deemed eligible to proceed with high-dose chemotherapy and autologous stem cell transplantation by local transplant center Patients who have undergone autologous stem cell transplantation within 3 months from study entry AIDS-related non-Hodgkin lymphoma and other non-Hodgkin lymphoma* Failed standard first-line therapy; and* Failed autologous stem cell transplant if indicated for histology (i.e diffuse large B-cell lymphoma) or autologous stem cell transplant is not feasible Stem cell transplant (SCT): no evidence of active graft vs. host disease for at least 4 weeks; for allogeneic SCT patients, >= 3 months must have elapsed since transplant* Must have received no more than 1 prior autologous or allogeneic stem cell transplant.* Patients must be off all systemic immunosuppressive therapy for at least 2 weeks, excluding hydrocortisone for physiologic cortisol replacement Patients who have undergone allogeneic stem cell transplantation and have required systemic treatment for GVHD (including but not limited to oral or parenteral corticosteroids, ibrutinib, and extracorporeal phototherapy) within the last 12 weeks Must not have received any prior stem cell transplant Patients with a history of allogeneic hematopoietic stem cell transplantation (HSCT) will be eligible if they are more than 90 days removed from the date of stem cell infusion, have no evidence of acute graft-versus-host disease (GVHD) or active chronic (grade 2-4) GVHD, and are off of all transplant-related immunosuppression for at least 2 weeks Allowed prior allogeneic hematopoietic stem cell transplantation (allo-HCT) regardless of stem cell source; patients must be at least 3 months post allo-HCT (at time of treatment start); mismatched transplantations would be allowed Patients must meet institutional eligibility requirements for stem cell transplant, including cardiac, renal, liver, and pulmonary requirements Stem cell infusions (with or without total body irradiation [TBI]):* Allogeneic (non-autologous) bone marrow or stem cell transplant, or any stem cell infusion including donor lymphocyte infusion (DLI) or boost infusion: >= 84 days after infusion, and no evidence of graft-versus-host disease (GVHD)* Autologous stem cell infusion including boost infusion: >= 42 days Any patients eligible for allogeneic stem cell transplantation (allo-SCT) and willing to undergo allo-SCT as determined at time of screening for trial; patients who are ineligible or not interested in undergoing allo-SCT will be eligible for the trial Patients with subependymal giant cell astrocytomas (SEGAs) are not eligible