AMC 120, Glofitamab Plus Chemoimmunotherapy in Newly Diagnosed HIV-Associated Large B-Cell Lymphoma (The "Glofit-RCHOP Study")

Inclusion Criteria: * Participant is able to understand and willing to sign a written informed consent document * Participants must have histologically (via at least a core or ideally, incisional or excisional biopsy) documented CD20 positive newly diagnosed HIV-associated LBCL as per World Health Organization (WHO) 5th edition, diffuse large B-cell lymphoma (DLBCL), not otherwise specified (NOS); high grade B-cell lymphoma-NOS or DLBCL/high grade B-cell lymphoma with MYC and BCL2 rearrangement. Plasmablastic lymphoma and primary effusion lymphoma may be included only if CD20-positive * Stage II-IV disease (as per Lugano Staging Criteria) that is measurable as defined below: * Measurable lymph nodes with longest diameter \> 1.5 cm, or * Measurable extranodal lesions with longest diameter \> 1.0 cm * Participants with bone marrow involvement only will be eligible as long as the morphological bone marrow involvement is documented on a bone marrow biopsy. These participants, however, will need to be willing to undergo subsequent bone marrow biopsies for response assessment and documentation * Evidence of HIV infection. Participants must have documentation of HIV-1 infection by means of any one of the following: * Documentation of HIV diagnosis in the medical record by a licensed health care provider; * Documentation of receipt of ART (at least two different medications that do not constitute a prescription for pre-exposure prophylaxis) by a licensed health care provider. Documentation may be a record of an ART prescription in the participant's medical record, a written prescription in the name of the participant for ART, or pill bottles for ART with a label showing the participant's name; * HIV-1 ribonucleic acid (RNA) detection by a licensed HIV-1 RNA assay at any time; * Any licensed HIV screening antibody and/or HIV antibody/antigen combination assay confirmed by a second licensed HIV assay such as a HIV-1 Western blot confirmation or HIV rapid multispot antibody differentiation assay. * Note: The term "licensed" refers to a kit that has been certified or licensed by an oversight body within the participating country and validated internally (e.g., United States \[US\] Food and Drug Administration \[FDA\]). World Health Organization and Centers for Disease Control and Prevention guidelines mandate that confirmation of the initial test result must use a test that is different from the one used for the initial assessment. A reactive initial rapid test should be confirmed by either another type of rapid assay or an E/CIA that is based on a different antigen preparation and/or different test principle (e.g., indirect versus competitive), or a Western blot or a plasma HIV-1 RNA viral load. * Participants with HIV must be on treatment with effective ART that is in accordance with the current International AIDS Society guidelines concurrently with chemotherapy. Use of experimental antiretroviral agents or those containing zidovudine (including Combivir and Trizivir) or ritonavir (includes Norvir® or Kaletra®), cobicistat, didanosine (Videx® or Videx EC®), or similar potent CYP3 inhibitors are prohibited. In order to be eligible, participants taking zidovudine or ritonavir, cobicistat, didanosine, or other CYP3 inhibitors must change to a different regimen 7 days prior to protocol therapy initiation. Changes to ART therapy during the study may be made if medically necessary (toxicity, failure of regimen, etc.). Participants must be on ART for at least 7 days prior to initiation of protocol therapy except for ART-naïve participants who need to get started on ART within the 1st cycle of study treatment (before cycle 2 day 1). ART needs to be approved by protocol chair or co-chair prior to enrollment * Age ≥ 18 years. Because no dosing or adverse event (AE) data are currently available on the use of glofitamab in combination with RCHOP (rituximab, cyclophosphamide, doxorubicin, vincristine, and prednisone) in participants \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥50%) * Absolute neutrophil count (ANC) ≥ 1,000/mcL unless decreased due to bone marrow involvement. Also, in participants with the Duffy antigen null phenotype, neutrophil counts may be lower and a lower threshold required for enrollment can be discussed with the protocol chair on a case-by-case basis * Platelets ≥ 75,000/mcL unless decreased due to bone marrow involvement * Hemoglobin of ≥ 8 g/dL unless decreased due to bone marrow involvement * Aspartate aminotransferase (AST \[serum glutamic oxaloacetic transaminase (SGOT)\])/alanine aminotransferase (ALT \[serum glutamate pyruvate transaminase (SGPT)\]) ≤ 3 × institutional upper limit of normal (ULN; ≤ 5 × ULN is acceptable if secondary to liver involvement by lymphoma) * Total serum bilirubin ≤ 1.5 × institutional ULN (\< 3.0 × ULN for participants with Gilbert syndrome). If, however, the elevated bilirubin is felt to be secondary to ART, the total bilirubin must be ≤ 3.5 mg/dL, provided that the direct bilirubin is normal and the AST and ALT ≤ 3 x the ULN * Glomerular filtration rate (GFR) no lower than 30 mL/min/1.73 m\^2. GFR can be measured directly or estimated using the site's institutional standards * Participants must have adequate cardiac function defined as a left ventricular ejection fraction of at least 45% as determined by echocardiogram or multigated acquisition within 6 weeks before enrollment * The effects of glofitamab on the developing human fetus are unknown. For this reason and because CD20/CD3 bispecific antibodies, as well as other therapeutic agents used in this trial, are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; total abstinence) from study entry and for at least 1 months from the last glofitamab administration or 12 months from the l