Testing the Investigational Medication Combination of Daratumumab and Teclistamab Compared to the Usual Treatment (Daratumumab, Pomalidomide, Dexamethasone or Daratumumab, Carfilzomib, Dexamethasone) for Patients With High-risk Multiple Myeloma Refractory or in First Relapse

Inclusion Criteria: * Patient must be ≥ 18 years of age * Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0-2 (PS 3 allowed if secondary to pain) * Patient must have an identifiable dominant sequence (clonotype) established based on Adaptive Biotechnologies clonoSEQ® assay * Patient must have received only one prior line of therapy * One prior line of systemic therapy is defined as 1 or more cycles of single agent or combination therapy, as well as a 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 +/- proteasome inhibitor or anti-CD38 monoclonal antibody \[mAb\] maintenance therapy would be considered 1 line of prior therapy) * NOTE: Autologous stem cell transplant is allowed provided the stem cell infusion was \> 90 days prior to randomization. Allogeneic stem cell transplantation (SCT) patients are ineligible * Patient must be diagnosed with relapsed or refractory (RR) multiple myeloma, as defined by disease progression, either an increase in serum or urine M protein of any level, or other evidence of progression biochemical or clinical as specified in the IMWG progression criteria (including disease which becomes non-responsive or progressive on therapy or within 60 days of the last treatment in patients who had achieved a partial response or better on prior therapy) * Patient must be daratumumab-hyaluronidase (or isatuximab) naïve or daratumumab-hyaluronidase (or isatuximab) sensitive and \> 180 days from their last dose of daratumumab-hyaluronidase (or isatuximab) at the time of randomization * Patient must have high-risk multiple myeloma (HR-MM) as defined by one of the following either at diagnosis or at refractory status or at first relapse: * Evidence of deletion 17p by fluorescence in situ hybridization (FISH) testing on bone marrow * Evidence of t(4;14) by FISH testing on bone marrow * Evidence of t(14;16) by FISH testing on bone marrow * Evidence of t(14;20) by FISH testing on bone marrow * Evidence of chromosome 1 abnormalities either gain/amp 1q or deletion 1p by FISH testing on bone marrow OR * Evidence of non-hyperdiploid karyotype OR * Revised International Staging System (R-ISS) stage III beta2 microglobulin ≥ 5.5 mg/L and serum lactate dehydrogenase (LDH) \> institutional upper limit of normal (ULN) OR * Patient in first relapse and ≤ 24 months from the start of induction for both allogeneic stem cell transplantation (ASCT) eligible or ASCT ineligible patients (regardless of FISH, cytogenetic or RISS stage) * Patient must have measurable disease as defined by having one or more of the following, obtained within 28 days prior to randomization: * Serum M protein ≥ 0.5 g/dL (≥ 5 g/L) * Urine M protein ≥ 200 mg/24 hours * Serum free light chain (FLC) assay: Involved free light chain level ≥ 10 mg/dL (≥ 100 mg/L) provided serum FLC ratio is abnormal (\< 0.26 or \> 1.65) * Exception: patients without measurable disease in the serum or urine, but with bone or soft tissue plasmacytoma(s) ≥ 2 cm or who have bone marrow plasma cells ≥ 30% are eligible on study * Patient must have serum protein electrophoresis (SPEP), urine protein electrophoresis (UPEP), and serum FLC assays along with bone marrow biopsy or aspirate performed within 28 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. If both serum and urine M-components are measurable, both must be followed in order to confirm response * NOTE: The serum free light chain test is required to be done at each cycle * Patient must not have any known allergies, hypersensitivity, or intolerance to corticosteroids, monoclonal antibodies or human proteins, or their excipients (refer to respective package inserts or investigator's brochure), or known sensitivity to mammalian-derived products * Patients who have received prior systemic therapy for myeloma, including experimental therapy and steroids must have recovered from clinically significant adverse events prior to randomization * Patient may not be on steroids (prednisone \> 40mg/day or equivalent) at the time of randomization * Patient may have received prior palliative and/or localized radiation, provided that it is completed by the time of randomization * Patient must have the ability to understand and the willingness to sign a written informed consent document. Patients with impaired decision-making capacity (IDMC) who have a legally authorized representative (LAR) or caregiver and/or family member available will also be considered eligible * Absolute neutrophil count (ANC) ≥ 1,000/uL (=\< 28 days prior to protocol randomization) * Untransfused platelet count ≥ 50,000/uL (for patients with ≥ 50% plasma cells in the marrow) and untransfused platelet count \> 75,000/uL (for patients with \< 50% plasma cells in the marrow) (=\< 28 days prior to protocol randomization) * Untransfused hemoglobin ≥ 8.0 g/dL (=\< 28 days prior to protocol randomization) * Total bilirubin ≤ 1.5 x institutional ULN (upper limit of normal) (=\< 28 days prior to protocol randomization) * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3.0 × institutional ULN (=\< 28 days prior to protocol randomization) * Calculated creatinine clearance \> 30 mL/min (=\< 28 days prior to protocol randomization) * NOTE: Cockcroft-Gault equation should be used to calculate creatinine clearance * Patient must not be pregnant or breast-feeding due to the potential harm to an unborn fetus and possible risk for adverse events in nursing infants with the treatment regimens being used * All patients of childbearing potential must have a blood test or urine study within 14 prior to randomization to rule out pregnancy. Patients randomized to Arm A and to receive the daratumumab-hyaluronidase, pomalidomide, dexamethasone (DPd) regimen must also have a second pregnancy test within 24 hours prior to the first dose of pomalidomide and agree to ongoing pregnancy testing while on protocol treatment * A patient of childbearing potential is defined as anyone, regardless of 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) * Patient must not expect to conceive or father children by using accepted and effective method(s) of contraception or by abstaining from sexual intercourse for the duration of their participation in the study and for 5 months after the last dose of protocol treatment for patients on Arm B and for 3 months after the last dose of protocol treatment for patients on Arm A. In addition, patients randomized to Arm A and receive the daratumumab-hyaluronidase, pomalidomide, dexamethasone (DPd) regimen must also agree to register to the mandatory Risk Evaluation and Mitigation Strategies (REMS®) program and be willing and able to comply with the requirements of the REMS program. All patients must not breastfeed while on protocol treatment and for patients on Arm B they must not breastfeed for an additional 5 months after the last dose of protocol treatment * Patient may have primary plasma cell leukemia (pPCL), secondary plasma cell leukemia (sPCL) or extramedullary myeloma (EMM) * Patient must not have evidence of active or untreated central nervous system (CNS) positive MM. Patients with prior CNS involvement are eligible provided they had demonstrated evidence of CNS disease resolution by imaging and/or 2 consecutively negative cerebrospinal fluid (CSF) samples for the presence of plasma cells * Patient must not have active autoimmune disease * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of randomization are eligible for this trial * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better * Patients with a history of chronic obstructive pulmonary disease (COPD) must have forced expiratory volume in 1 second (FEV1) testing done within 28 days prior to randomization and the forced expiratory volume in 1 second (FEV1) must be \>= 50% of predicted normal * Patient must not have moderate or severe persistent asthma within 2 years prior to randomization * NOTE: Patients who currently have controlled intermittent asthma or controlled mild persistent asthma are eligible * Investigator must declare the intended chemotherapy regimen at the time of randomization should their patient be randomized to Arm A from the two options