Inclusion Criteria:  Histologically confirmed plasmablastic lymphoma according to WHO 2017, CD38-positive by immunohistochemistry (≥5% of positive cells) Local diagnosis of PBL and local CD38 assessment ≥5% will suffice for enrollment and start of treatment.  Patients with plasmablastic lymphoma relapsed or refractory:  after at least one line of conventional-dose chemotherapy followed or not by autologous stem cell transplantation; after at least one line of conventional-dose chemotherapy and not eligible for salvage autologous or allogeneic transplantation; ECOG Performance Status ≤ 3; Age ≥ 18 years; Both HIV-negative and HIV-positive patients are eligible; HIV infection responsive to ongoing cART (combination antiretroviral therapy);  At least one measurable disease lesion identifiable by imaging:  A nodal lesion must be at least 11 mm x 11 mm OR ≥ 16 mm in the greatest transverse diameter (regardless of short axis measurement). An extranodal lesion must be at least 10 mm x 10 mm.  Women of childbearing potential (WOCBP) and men must agree to use effective contraception if sexually active. This applies for the time period between signing of the informed consent form and 7 months (for women) o 4 months (for men) after last administration of bortezomib or 6 months after last daratumumab dose, regardless of sex. A woman is considered of childbearing potential, i.e., fertile, following menarche and until becoming postmenopausal unless permanently sterile. Permanent sterilization methods include but are not limited to hysterectomy, bilateral salpingectomy and bilateral oophorectomy. A postmenopausal state is defined as no menses for continuous 12 months without an alternative medical cause. A high follicle stimulating hormone (FSH) level in the postmenopausal range may be used to confirm a postmenopausal state in women not using hormonal contraception or hormonal replacement therapy. The investigator or a designated associate is requested to advise the patient how to achieve highly effective birth control method (failure rate of less than 1%) e.g., intrauterine device (IUD), intrauterine hormone-releasing system (IUS), bilateral tubal occlusion, vasectomized partner, and sexual abstinence. The use of condoms by male patients is required unless the female partner is permanently sterile.  WOCBP must have two negative pregnancy tests as verified by the study doctor prior to starting study therapy and must agree to undergo monthly pregnancy testing during the course of the study and after end of study therapy if clinically indicated. This applies even if the subject practices complete abstinence from heterosexual contact.  Subject understands and voluntarily signs and dates an informed consent form approved by an Independent Ethics Committee (IEC), prior to the initiation of any screening or study-specific procedures Subject must be able to adhere to the study visit schedule and other protocol requirements  Exclusion Criteria:  Histologic diagnosis different from confirmed plasmablastic lymphoma according to WHO 2017 and/or CD38 expression < 5% of positive cells CNS involvement Patients with known hypersensitivity to the investigational drug or to product components or severe allergic or anaphylactic reactions to humanized products Subject has received any anti-cancer therapy including chemotherapy, immunotherapy, radiotherapy, investigational therapy including targeted small molecule agents within 14 days prior to the first dose of study drug Concomitant Kaposi sarcoma; however, patients with only skin involvement of KS can be included.  Subject is:  Seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen [HBsAg]. Subjects with resolved infection (i.e., subjects who are HBsAg negative but positive for antibodies to hepatitis B core antigen [HBcAb] ± antibodies to hepatitis B surface antigen [HBsAb]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) DNA levels. Those who are PCR positive will be excluded. EXCEPTION: Subjects with serologic findings suggestive of HBV vaccination (HBsAb 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 Known to be seropositive for hepatitis C (except in the setting of a sustained virologic response [SVR], defined as aviremia at least 12 weeks after completion of antiviral therapy) Any history of another cancer during the last 5 years with the exception of non-melanoma skin tumors, in situ cervical carcinoma, or in situ breast cancer treated with curative intent with no history of metastatic disease. Chronic or ongoing active infectious disease requiring systemic treatment such as, but not limited to, chronic renal infection, chronic chest infection with bronchiectasis or tuberculosis. Drugs for HIV treatment are allowed, as per local investigator prescription. Active ongoing infection from SARS-CoV-2.  Screening laboratory values (due to causes different than lymphoma):  Absolute neutrophil count (ANC) <1.0 x 109/L (unless secondary to documented marrow involvement by lymphoma) Platelet count <75 x 109/L Hemoglobin < 7.5 g/dL Alanine aminotransferase (ALT) and/or Aspartate aminotransferase (AST) > 3.5 times the upper limit of normal (ULN) Alkaline phosphatase > 3.5 times ULN Bilirubin > 2 times x ULN (unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin) Serum Creatinine Clearance < 20 ml/h  Subject has clinically significant cardiac disease, including:  Myocardial infarction within 6 months before date of registration, or unstable or uncontrolled disease/condition related to or affecting cardiac function (e.g., unstable angina, congestive heart failure, New York Heart Association Class III-IV) Cardiac arrhythmia (Common Terminology Criteria for Adverse Events [CTCAE] current version Grade 2 or higher) or clinically significant ECG abnormalities. Screening 12-lead ECG showing a baseline QT interval as corrected by Fridericia's formula (QTcF) > 470 msec Evidence of any other clinically significant uncontrolled condition(s) Significant history of neurologic, psychiatric, endocrinological, metabolic, immunologic, or hepatic disease that would preclude participation in the study or compromise ability to give informed consent Breastfeeding women or women with a positive pregnancy test at screening