Daratumumab, Bortezomib, and Dexamethasone With or Without Venetoclax in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * PHASE I (ARMS A, B, C) - STEP 1: Eastern Cooperative Oncology Group (ECOG) performance status of 0-2. * PHASE I (ARMS A, B, C) - STEP 1: Patients must have been diagnosed with symptomatic relapsed/refractory multiple myeloma. * NOTE: Relapsed/refractory myeloma is defined as a disease which becomes non-responsive or progressive on therapy or within 60 days of the last treatment in patients who had achieved a minimal response (MR) or better on prior therapy. * PHASE I (ARMS A, B, C) - STEP 1: t(11;14) status must be determined. * PHASE I (ARMS A, B, C) - STEP 1: Patients must not have bortezomib refractory disease. Prior lenalidomide refractory patients are allowed. * PHASE I (ARMS A, B, C) - STEP 1: Patients must have been treated with 1 or more lines of therapy. 1 prior line of systemic therapy is defined as 1 or more planned cycles of single agent or combination therapy, as well as a planned series of treatment regimens administered in a sequential manner (e.g. lenalidomide, bortezomib and dexamethasone induction therapy for 4 cycles followed by autologous stem cell transplantation and then lenalidomide maintenance therapy would be considered 1 line of prior therapy). Auto stem cell transplant is allowed provided the patient is 100 days out from stem cell infusion. Patients must not have had prior venetoclax. Allogeneic stem cell transplantation (SCT) patients are excluded. * PHASE I (ARMS A, B, C) - STEP 1: Patients must have measurable disease as defined by having one or more of the following, obtained within 14 days prior to randomization: * \>= 0.5 g/dL monoclonal protein (M-protein) on serum protein electrophoresis. * \>= 200 mg/24 hrs of monoclonal protein (M-protein) on a 24 hour urine protein electrophoresis. * Involved free light chain \>= 10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio (\< 0.26 or \> 1.65). * PHASE I (ARMS A, B, C) - STEP 1: Serum protein electrophoresis (SPEP), urine protein electrophoresis (UPEP), and serum free light chain (FLC) assay are required to be performed within 14 days prior to randomization. * NOTE: UPEP (on a 24 hour collection) is required, no substitute method is acceptable. Urine must be followed monthly if the baseline urine M-spike is \>= 200 mg/24 hr and urine in addition to serum must be followed in order to confirm a very good partial response (VGPR) or higher response. * NOTE: The serum free light chain test is required to be done if the patient does not have measurable disease in the serum or urine. Measurable disease in the serum is defined as having a serum M-spike \>= 0.5 g/dL. Measurable disease in the urine is defined as having a urine M-spike \>= 200 mg/24 hr. * PHASE I (ARMS A, B, C) - STEP 1: Platelet count \>= 100,000 cells/mm\^3 (within 14 days prior to randomization). * PHASE I (ARMS A, B, C) - STEP 1: Absolute neutrophil count \>= 1000 cells/mm\^3 (within 14 days prior to randomization). * PHASE I (ARMS A, B, C) - STEP 1: Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x the upper limit of normal (within 14 days prior to randomization). * PHASE I (ARMS A, B, C) - STEP 1: Total bilirubin =\< 1.5 x the upper limit of normal (within 14 days prior to randomization). * PHASE I (ARMS A, B, C) - STEP 1: Calculated creatinine clearance \>= 30 mL/min (within 14 days prior to randomization). * PHASE I (ARMS A, B, C) - STEP 1: Hemoglobin \>= 8.0 g/dL (within 14 days prior to randomization). * PHASE I (ARMS A, B, C) - STEP 1: Women must not be pregnant or breast-feeding due to risk of fetal harm by the chemotherapeutic agents prescribed in this protocol. All females of childbearing potential must have a blood test or urine study within 7 days prior to registration to rule out pregnancy. A female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). * PHASE I (ARMS A, B, C) - STEP 1: Women of childbearing potential and sexually active males must use an accepted and highly effective method(s) of contraception or abstain from sexual intercourse for the duration of their participation in the study and for 3 months after the last dose of daratumumab or 30 days after the last dose of venetoclax, whichever is longer. Male patients must also agree not to donate sperm for the duration of their participation in the study for 3 months after the last dose of daratumumab or 30 days after the last dose of venetoclax whichever is longer. * PHASE I (ARMS A, B, C) - STEP 1: Patients must not have \> grade 2 neuropathy and/or a syndrome characterized by polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin change (POEMS). * PHASE I (ARMS A, B, C) - STEP 1: Patients must not have New York Heart Association (NYHA) class III or IV heart failure or myocardial infarction within 6 months prior to registration. * PHASE I (ARMS A, B, C) - STEP 1: Patients must avoid concomitant use of venetoclax with moderate or strong CYP3A inhibitors, strong or moderate CYP3A inducers, P-glycoprotein (P-gp) inhibitors, or narrow therapeutic index P-gp substrates. * PHASE I (ARMS A, B, C) - STEP 1: Patients must not be seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen \[HBsAg\]). Patients with resolved infection (i.e., patients who are HBsAg negative but positive for antibodies to hepatitis B core antigen \[anti-HBc\] and/or antibodies to hepatitis B surface antigen \[anti-HBs\]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HepB) deoxyribonucleic acid (DNA) levels. Those who are PCR positive are not eligible. Patients with serologic findings suggestive of HepB vaccination (anti-HBs positivity as the only serologic marker) AND a known history of prior HepB vaccination, do not need to be tested for HepB DNA by PCR. Patients with HepB core antibody (cAb) positive but HepB sAg negative, as well as HepB PCR negative, are eligible but will need to be monitored throughout the study. * PHASE I (ARMS A, B, C) - STEP 1: Patients must not be seropositive for hepatitis C (except in the setting of a sustained virologic response \[SVR\], defined as aviremia at least 12 weeks after completion of antiviral therapy). * PHASE II (ARMS D, E) - STEP 1: ECOG performance status of 0-2. * PHASE II (ARMS D, E) - STEP 1: Patients must have been diagnosed with symptomatic relapsed/refractory multiple myeloma. * NOTE: Relapsed/refractory myeloma is defined as a disease which becomes non-responsive or progressive on therapy or within 60 days of the last treatment in patients who had achieved a minimal response (MR) or better on prior therapy. * PHASE II (ARMS D, E) - STEP 1: t(11;14) status must be determined. * PHASE II (ARMS D, E) - STEP 1: Patients must not have bortezomib refractory disease. Prior lenalidomide refractory patients are allowed. * PHASE II (ARMS D, E) - STEP 1: Patients must have been treated with 1 or more lines of therapy. 1 prior line of systemic therapy is defined as 1 or more planned cycles of single agent or combination therapy, as well as a planned series of treatment regimens administered in a sequential manner (e.g. lenalidomide, bortezomib and dexamethasone induction therapy for 4 cycles followed by autologous stem cell transplantation and then lenalidomide maintenance therapy would be considered 1 line of prior therapy). Auto stem cell transplant is allowed provided the patient is 100 days out from stem cell infusion. Patients must not have had prior venetoclax. Allogeneic SCT patients are excluded. * PHASE II (ARMS D, E) - STEP 1: Patients must have measurable disease as defined by having one or more of the following, obtained within 14 days prior to randomization: * \>= 0.5 g/dL monoclonal protein (M-protein) on serum protein electrophoresis. * \>= 200 mg/24 hours (hrs) of monoclonal protein (M-protein) on a 24 hour urine protein electrophoresis. * Involved free light chain \>= 10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio (\< 0.26 or \> 1.65). * PHASE II (ARMS D, E) - STEP 1: SPEP, UPEP, and serum FLC assay are required to be performed within 14 days prior to randomization. * NOTE: UPEP (on a 24 hour collection) is required, no substitute method is acceptable. Urine must be followed monthly if the baseline urine M-spike is \>= 200 mg/24 hr. Please note that if both serum and urine m-components are present, both must be followed in order to evaluate response. * NOTE: The serum free light chain test is required to be done if the patient does not have measurable disease in the serum or urine. Measurable disease in the serum is defined as having a serum M-spike \>= 0.5 g/dL. Measurable disease in the urine is defined as having a urine M-spike \>= 200 mg/24 hr. * PHASE II (ARMS D, E) - STEP 1: Platelet count \>= 100,000 cells/mm\^3 (within 14 days prior to randomization). * PHASE II (ARMS D, E) - STEP 1: Absolute neutrophil count \>= 1000 cells/mm\^3 (within 14 days prior to randomization). * PHASE II (ARMS D, E) - STEP 1: AST and ALT =\< 2.5 x the upper limit of normal (within 14 days prior to randomization). * PHASE II (ARMS D, E) - STEP 1: Total bilirubin =\< 1.5 x the upper limit of normal (within 14 days prior to randomization). * PHASE II (ARMS D, E) - STEP 1: Calculated creatinine clearance \>= 30 mL/min (within 14 days prior to randomization). * PHASE II (ARMS D, E) - STEP 1: Hemoglobin \>= 8.0 g/dL (within 14 days prior to randomization). * PHASE II (ARMS D, E) - STEP 1: Women must not be pregnant or breast-feeding due to risk of fetal harm by the chemotherapeutic agents prescribed in this protocol. All females of childbearing potential must have a blood test or urine study within 7 days prior to registration to rule out pregnancy. A female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). * PHASE II (ARMS D, E) - STEP 1: Women of childbearing potential and sexually active males must use an accepted and highly effective method(s) of contraception or abstain from sexual intercourse for the duration of their participation in the study and for 3 months after the last dose of daratumumab or 30 days after the last dose of venetoclax, whichever is longer. Male patients must also agree not to donate sperm for the duration of their participation in the study for 3 months after the last dose of daratumumab or 30 days after the last dose of venetoclax, whichever is longer. * PHASE II (ARMS D, E) - STEP 1: Patients must not have \> grade 2 neuropathy and/or POEMS. * PHASE II (ARMS D, E) - STEP 1: Patients must not have NYHA Class III or IV heart failure or myocardial infarction within 6 months prior to registration. * PHASE II (ARMS D, E) - STEP 1: Patients must avoid concomitant use of venetoclax with moderate or strong CYP3A inhibitors, strong or moderate CYP3A inducers, P-gp inhibitors, or narrow therapeutic index P-gp substrates. * PHASE II (ARMS D, E) - STEP 1: Patients must not be seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen \[HBsAg\]). Patients with resolved infection (i.e., patients who are HBsAg negative but positive for antibodies to hepatitis B core antigen \[anti-HBc\] and/or antibodies to hepatitis B surface antigen \[anti-HBs\]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HepB) DNA levels. Those who are PCR positive are not eligible. Patients with serologic findings suggestive of HepB vaccination (anti-HBs positivity as the only serologic marker) AND a known history of prior HepB vaccination, do not need to be tested for HepB DNA by PCR. Patients with HepB cAb positive but HepB sAg negative, as well as HepB PCR negative, are eligible but will need to be monitored throughout the study. * PHASE II (ARMS D, E) - STEP 1: Patients must not be seropositive for hepatitis C (except in the setting of a sustained virologic response \[SVR\], defined as aviremia at least 12 weeks after completion of antiviral therapy). However, patients who test negative for HepC by PCR may participate.