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 last rituximab administration, whichever is the longest. Women of childbearing potential, defined as pre- or perimenopausal females with an intact uterus, must have a negative serum β-HCG within 7 days prior to enrollment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform the treating physician immediately. Men treated with glofitamab must also agree to use adequate contraception with partners who are women of childbearing potential (condom plus an additional contraceptive method, such as bilateral tubal occlusion, male sterilization, hormone-releasing intrauterine devices, and copper intrauterine devices) or use contraceptive measures such as a condom with pregnant female partners to avoid exposing the embryo during intercourse, from study entry, for the duration of study participation, and 1 months after the last glofitamab dose or 12 months after completion of rituximab administration, whichever is the longest * Any CD4 count is allowed * Participants with leptomeningeal disease are eligible if the treating physician determines that immediate central nervous system (CNS) specific treatment is not required and is unlikely to be required during the first cycle of therapy, except during the initial safety run-in phase, during which participants with leptomeningeal disease will be excluded. For the first three study participants, enrollment will be halted until the third participant completes two target doses (30 mg) of glofitamab and dose-limiting toxicity (DLT) assessment is completed * Participants 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 Exclusion Criteria: * Participants who are receiving any other investigational agents * Participants with active parenchymal central nervous system (CNS) lymphomatous involvement are excluded; however, asymptomatic leptomeningeal disease is allowed as long as participants have ongoing CNS directed therapy, except during the initial safety-run in phase, during which participants with leptomeningeal disease will also be excluded * History of allergic reactions attributed to compounds of similar chemical or biologic composition to agents used in study * Uncontrolled intercurrent illness including, but not limited to: symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, significant pulmonary disease (including, but not limited to clinically significant obstructive pulmonary disease or history of bronchospasm), clinically significant liver disease (including viral or other hepatitis or cirrhosis) or psychiatric illness/social situations that, in the opinion of the investigator, would limit compliance with study requirements or make participation in this protocol unreasonably hazardous * Because there is an unknown but potential risk for AEs in nursing infants secondary to treatment of the mother with the study agent(s), breastfeeding should be discontinued if the mother is treated with the study agent(s). These potential risks may also apply to other agents used in this study * Participants with refractory HIV disease will not be eligible. Refractory HIV will be defined as prior ART exposure and HIV viral load \> 1000 copies/uL and no options for HIV control evaluated by HIV genotyping. Participants with HIV viral load \> 1000 copies/uL can be enrolled if additional ART will be initiated * Participants who have had chemotherapy other than allowable pre-trial therapy outlined below, or radiotherapy other than palliative radiation for medical emergencies (i.e., cord compression or impending fracture), within the last four weeks. * Allowable prior therapy: * A maximum of one cycle of combination chemotherapy, including CHOP ± rituximab and etoposide-prednisone-Oncovin-cyclophosphamide-hydroxydaunorubicin (EPOCH) ± rituximab. The start of previous chemotherapy cycle must occur at least 21 days but no more than 35 days prior to beginning treatment under this protocol, and this cycle will count towards the maximum of six cycles under this study (i.e., cycle received prior to study enrollment will count as cycle 1) OR * One prior course of limited therapy including cyclophosphamide and/or glucocorticoids and/or rituximab to improve fitness for combination chemotherapy (i.e., those with impaired hepatic function, renal function and or performance status due to lymphomatous involvement). The start of this therapy may occur up to 35 days prior to beginning treatment under this protocol; cyclophosphamide administration must have been completed at least 14 days prior to initiation of protocol therapy. Such treatment will not count towards the maximum of six cycles under this study (i.e., participants will receive six cycles on study and start with cycle 1 of RCHOP) * Participants must not have had previous anthracycline treatment within the last two years, except for one cycle off protocol or liposomal doxorubicin. Any prior exposure to liposomal doxorubicin is allowed as long as the left ventricular ejection fraction is ≥ 45%. It is at the discretion of the investigator if prior exposure to doxorubicin more than two years prior is acceptable * Participants with active tuberculosis and other active opportunistic infections requiring active treatment * Participants with active fungal infection or history of opportunistic infection requiring continuous prophylaxis or treatment with fluconazole, voriconazole or posaconazole. Oral candidiasis or fungal nail bed infections are permitted * Participants with chronic hepatitis B (defined by a positive test for hepatitis B surface antigen \[HBsAg\]). All participants will be required to be screened for Hepatitis B. Participants with resolved infection (i.e., participants 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 (HBV) DNA levels. Participants who are PCR positive will be excluded. EXCEPTION: Participants with serologic findings suggestive of HBV vaccination (anti-HBs positivity as the only serologic marker) AND a known history of prior HBV vaccination, do not need to be tested for HBV DNA by PCR. For participants who have evidence of prior Hepatitis B exposure and are PCR negative, hepatitis B (Hep B) reactivation prophylaxis is mandated using institutional guidelines * If hepatitis C antibody positive, participants will be excluded from study unless hepatitis C viral load is undetectable. Additionally, participants must have no evidence of cirrhosis and have liver function tests (LFTs) * Participants with baseline peripheral neuropathy \> grade 2 or painful \>/= grade 2 neuropathy * Participants who have not recovered from AEs due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the exception of alopecia * Concomitant medications: Participants should only be excluded from trial participation when clinically relevant known or predicted drug-drug interactions or potential overlapping toxicities will impact safety or efficacy. Please include scientific or clinically based rationale for exclusion. * Please note that this must account for all agents to be used on this study, including commercial agents. Please refer to the FDA product labels for all commercial agents and include information on prohibited concomitant medications in all applicable sections of the protocol * A wash out period prior to the start of cycle 1 of at least 4 weeks for prior use of any monoclonal antibody, systemic immunotherapeutic agents, immunosuppressive agents (such as, but not limited to cyclosporin, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor) is required * Unable to comply with the requirements of the protocol, or unable to provide adequate informed consent in the opinion of the principal investigator (PI) * Major surgery, other than diagnostic surgery, occurring within 4 weeks prior to study entry. Splenectomy will not be considered an exclusionary major surgery * Having received a live, attenuated vaccine within 28 days prior to registration * Myocardial infarction within the preceding 3 months * Prior solid organ or allogeneic hematopoietic cell transplant * Prior diagnosis of progressive multifocal leukoencephalopathy (PML) * Known or suspected history of hemophagocytic lymphohistiocytosis (HLH) * History of autoimmune disease, including but not limited to myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener granulomatosis, Sjögren syndrome, Guillain-Barré syndrome, multiple sclerosis, vasculitis, or glomerulonephritis. The following exceptions apply: * Patients with a history of autoimmune-related hypothyroidism on a stable dose of thyroid-replacement hormone * Patients with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for study * Patients with a history of disease-related immune thrombocytopenic purpura, autoimmune hemolytic anemia, or other stable autoimmune diseases * Participants with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., participants with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met: * Rash must cover \< 10% of body surface area * Disease is well controlled at baseline and requires only low-potency topical corticosteroids