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.