Inclusion Criteria:
* Participants must have histologically and immunophenotypically (via at least a core or ideally, incisional or excisional biopsy) documented plasmablastic lymphoma.
* Stage II-IV disease (Ann Arbor staging criteria) or stage I disease with elevated lactate dehydrogenase (LDH) or bulky tumor (\> 7.5 cm).
* Known HIV status. At most 7 HIV negative patients will be allowed on the study. Once 7 HIV negative patients have been enrolled, future enrollment will allow only HIV positive patients. Participants may be HIV positive, with documentation of HIV 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 highly active antiretroviral therapy (HAART) (at least three different medications) by a licensed health care provider (documentation may be a record of an HAART prescription in the participant?s medical record, a written prescription in the name of the participant for HAART, or pill bottles for HAART with a label showing the participant?s name);
* HIV-1 ribonucleic acid (RNA) detection by a licensed HIV-1 RNA assay demonstrating \>1000 RNA copies/mL;
* 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: A ?licensed? assay refers to a U.S. Food and Drug Administration (FDA)-approved assay, which is required for all Investigational New Drug (IND) studies.
* Participants without HIV infection must have evidence of a negative result using any licensed HIV screening antibody assay and/or HIV antibody/antigen combination assay.
* Participants must have measurable disease (unless marrow-only disease is present), defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter) as \>= 15 mm (\>= 1.5cm) by computed tomography (CT) or positron emission tomography (PET) scan or evaluable by bone marrow.
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 50%).
* Absolute neutrophil count \>= 1,000 cells/mcL unless decreased due to bone marrow involvement.
* Platelets \>= 75,000 cells/mcL unless decreased due to bone marrow involvement.
* Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (\< 3.0 x ULN for patients with Gilbert syndrome). If, however, the elevated bilirubin is felt to be secondary to antiretroviral therapy, the total bilirubin must be =\< 3.5 mg/dL, provided that the direct bilirubin is normal and the aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x the upper limit of normal.
* AST (serum glutamic oxaloacetic transaminase \[SGOT\])/ALT (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN (=\< 5 x ULN is acceptable if liver metastases are present).
* Creatinine =\< 1.5 x institutional ULN OR glomerular filtration rate (GFR) \>= 45 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal, as calculated by the Cockcroft-Gault formula.
* Adequate cardiac function defined as an ejection fraction on echocardiogram (ECHO) or multigated acquisition scan (MUGA) that is at or above 45%.
* CD4 count \>= 100 cell/mL for HIV-positive participants.
* If HIV-positive, participant must not have a history of acquired immunodeficiency syndrome (AIDS)-defining opportunistic infection within the past year.
* If HIV-positive, participant should have concurrent treatment with effective highly active antiretroviral therapy (HAART) or agree to start HAART.
* The effects of daratumumab on the developing human fetus are unknown. For this reason and because another monoclonal antibody (mAb), rituximab, crosses the placenta and 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; abstinence) prior to study entry, the duration of study participation, and 90 days after completion of therapy. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men with female partners treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 90 days after completion of daratumumab administration.
* Ability to understand and the willingness to sign a written informed consent document.
Exclusion Criteria:
1. Prior cytotoxic chemotherapy or radiotherapy for this lymphoma other than palliative radiation for medical emergencies (like cord compression) or the following chemotherapy:
• A maximum of one cycle of combination chemotherapy, including EPOCH or CHOP-like therapy. The start of the previous chemotherapy cycle must occur at least 21 days but no more than 28 days prior to the beginning of therapy under this protocol, and such cycle will count towards the maximum of 6 cycles under this study (i.e., cycle off study will count as cycle 1 in terms of feasibility determination as per primary endpoint).
OR
• One prior cycle of limited therapy including cyclophosphamide and/or glucocorticoids to improve performance status or hepatic or renal function impaired due to lymphoma involvement. The start of this therapy may occur up to 28 days prior to the beginning of study treatment under this protocol. Cyclophosphamide administration must have been completed at least 14 days prior to initiation of study treatment. Such treatment will not count towards the maximum of 6 cycles under this study (i.e., participants will receive 6 cycles on study).
2. Patients who are receiving any other investigational agents.
3. Participants must not have had previous anthracycline treatment within the last two years, except for liposomal doxorubicin. Any prior exposure to liposomal doxorubicin is allowed as long as the LVEF is ≥45%. It is at the discretion of the investigator if prior exposure to doxorubicin is acceptable.
4. Participants who have previously received daratumumab for another indication.
5. Participants must not be on cobicistat, indinavir, or ritonavir, or agents that are strong CYP3A4 inhibitors. If on a strong CYP3A4 inhibitor regimen prior to study enrollment, participants must be switched to alternative drugs at least one week prior to administration of study therapy.
6. Participants with peripheral neuropathy grade ≥ 3 or neuropathic pain grade ≥ 2.
7. Expected survival \< 2 months.
8. Participants with known brain metastases from solid tumors will be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events.
9. Patients with known or suspected parenchymal brain or spinal cord disease, and/or suspected or symptomatic leptomeningeal disease from lymphoma, prior to study enrolled will be excluded. Asymptomatic leptomeningeal disease only will be allowed.
10. Patients who are seropositive for 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 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.
11. Patients diagnosed with Hepatitis C who are Hepatitis C antibody positive, whether Hepatitis C RNA level is measurable or not, must have no evidence of cirrhosis and have liver function tests.
12. History of allergic reactions, hypersensitivity, or intolerance attributed to compounds of similar chemical or biologic composition to daratumumab, or other agents used in the study or known sensitivity to mammalian-derived products.
13. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
14. Pregnancy or breastfeeding. A pregnancy test must be performed within 7 days prior to therapy administration in women of childbearing potential. Pregnant women are excluded from this study because the effects of daratumumab on the developing human fetus are unknown. Immunoglobulin G1 (IgG1) monoclonal antibodies are transferred across the placenta. Based on its mechanism of action, daratumumab may cause fetal myeloid or lymphoid-cell depletion and decreased bone density. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with daratumumab, breastfeeding should be discontinued if the mother is treated with daratumumab. These potential risks may also apply to other agents used in this study. Both male and female participants must use effective methods of birth control during the course of the study and for 3 months after stopping daratumumab. Participants must also agree to not donate eggs or sperm while taking daratumumab and for 3 months after stopping.
15. Unable to comply with the requirements of the protocol, or unable to provide adequate informed consent in the opinion of the Principal Investigator.
16. Serious, ongoing, non-malignant disease or infection, which in the opinion of the investigator and/or the sponsor would compromise other protocol objectives. Participants with active opportunistic infections are ineligible.
17. Major surgery, other than diagnostic surgery, occurring 4 weeks prior to study entry. Splenectomy will not be considered an exclusionary major surgery.
18. Myocardial infarction (MI) within 6 months prior to study entry, New York Heart Association (NYHA) Class II or greater heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, clinically significant pericardial disease, or electrocardiographic evidence of acute ischemic or active conduction system abnormalities.
19. Either of the following:
* Known chronic obstructive pulmonary disease (COPD) with a forced expiratory volume in 1 second (FEV1) is \<50% of predicted normal. Note that FEV1 testing also is required for subjects suspected of having COPD and subjects must be excluded if FEV1 is \<50% of predicted normal.
* Known moderate or severe persistent asthma, or a history of asthma within the last 2 years, or currently has uncontrolled asthma of any classification. (Subjects who currently have controlled intermittent asthma or controlled mild persistent asthma are allowed to participate in the study.)
20. Participants with prior malignancies are ineligible unless:
* Treatment for the prior malignancy was completed at least 2 years prior to the lymphoma treatment start date and the participant has no evidence of the concurrent malignancy OR
* The concurrent malignancy is clinically stable and does not require tumor-directed treatment.
