A Trial of Anti-CD4 Antibody UB-421 in Combination With Optimized Background Antiretroviral Therapy in Patients With Multi-Drug Resistant HIV-1 Infection

* INCLUSION CRITERIA: In order to be eligible to participate in this study, an individual must meet all of the following criteria: * Ability to provide informed consent; * Stated willingness to comply with all study procedures and availability for the duration of the study; * Aged 18 years or older; * Have a life expectancy that is \>6 months (as judged by the Principal Investigator \[PI\]); * HIV-1 seropositive; * Have a history of being treated for at least 6 months with ART; * Plasma HIV-1 RNA \>= 1,000 copies/mL at the Screening visit; * Screening CD4+ T cell counts of \> 350 cells/mm3; * Documented genotypic or phenotypic resistance to at least one ARV drug within three or more drug classes of ARV medications; * Receiving a stable failing regimen of cART for at least 8 weeks before Screening and are willing to continue the failing regimen during the Screening Phase and up to study day 21 of the Treatment Phase, OR have failed a regimen within 8 weeks of Screening, are off ART and are willing to stay off ART until day 21 of the Treatment Phase. Patients who failed to attain or maintain complete suppression of plasma viremia while receiving fostemsavir will not be allowed to enroll in the study. Patients who failed to attain or maintain complete suppression of plasma viremia while receiving ibalizumab-based salvage regimen will be allowed to enroll in this study; however, prior ibalizumab use must have ended at least five half-lives (i.e., 21 days) before the first dose of UB-421; * Have viral sensitivity to at least one FDA-approved ARV agent, as determined by genotypic or phenotypic ARV drug resistance testing, and such agent can be used as a component of OBT. Patients currently receiving enfuvirtide, ibalizumab, or maraviroc will be excluded from this study, unless patients agree to discontinue these drugs for at least five half-lives (i.e., 1 day, 21 days or 4 days, respectively), before the first dose of UB-421. These drugs also will not be allowed as a component of OBT; * Be willing to remain on treatment without any changes or additions to the OBT regimen, except for toxicity management or upon meeting criteria for treatment failure; * For females of reproductive potential: use of highly effective contraception - as detailed in the Centers for Disease Control and Prevention (CDC) US Selected Practice Recommendations for Contraceptive Use (US SPR) - for at least 1 month prior to Baseline visit and agreement to use such a method during study participation and for an additional 4 weeks after the end of UB-421 administration. For males of reproductive potential, for at least 1 month prior to Baseline visit and agreement to use such a method during study participation and for an additional 4 weeks after the end of UB-421 administration: use of condoms or other methods to ensure effective contraception with partner of childbearing potential; Non-reproductive potential is defined as azoospermia, postmenopausal, surgical sterilization at least 6 weeks before screening, or a congenital or acquired condition that definitively prevents conception. Further, postmenopausal is defined as at least 12 consecutive months with no menses at age 50 or older, and also a high follicle-stimulating hormone level in postmenopausal range at ages 45-50 years, for participants not using hormonal contraception or hormone replacement therapy. Participants of reproductive potential must either practice complete and uninterrupted abstinence from heterosexual activity or use two of the following methods of contraception with their partners. The 2 methods must include one from each group, both of which must be consistently use: Barrier methods: * Diaphragm with spermicide (cannot be used in conjunction with cervical cap/spermicide). * Cervical cap with spermicide (only for nulliparous partners). * Contraceptive sponge (only for nulliparous partners). * Male or female condom (cannot be used together). Non-barrier methods: * Intrauterine device. * Hormonal contraception: pill (estrogen/progestin or progestin-only), skin patch, vaginal ring, rod implanted in the skin, or subcutaneous injection. -Laboratory values at Screening of: * Absolute neutrophil count (ANC) \>= 750/mm3; * Hemoglobin (Hb) \>= 10.5 gm/dL (male) or \>= 9.5 gm/dL (female); * Platelets \>= 50,000 /mm3; * Serum alanine transaminase (ALT) \< 2.5 x upper limit of normal (ULN); * Serum AST \< 2.5 x ULN; * Bilirubin (total) \< 2.5 x ULN (Exceptions: Gilbert's disease, or the subject is receiving atazanavir and there is no evidence of significant liver disease); * Estimated or a measured glomerular filtration rate \>60 mL/min/1.73 m2 as determined by the NIH CC laboratory. EXCLUSION CRITERIA: An individual who meets any of the following criteria will be excluded from participation in this study: * Chronic hepatitis B, as evidenced by a positive test for HBsAg, or chronic hepatitis C virus (HCV) infection, as evidenced by a positive test for HCV RNA. Subjects with a positive test for HCV antibody and a negative test for HCV RNA are eligible; * AIDS-defining Stage 3 opportunistic illnesses according to the Centers for Disease Control and Prevention (CDC) Classification System for HIV Infection \[11\] at or within 3 months of screening patients on maintenance therapy (for instance, for toxoplasmosis or cryptococcal infection can be recruited provided their diagnosis was not within 3 months of screening); * HIV immunotherapy (including broadly neutralizing HIV antibodies) within 12 weeks prior to screening; * Participation in an experimental drug trial(s) within 4 weeks prior to the Screening visit; * Pregnancy or lactation; * Any licensed or experimental vaccination (e.g., hepatitis B, influenza, pneumococcal polysaccharide) received within 2 weeks prior to study enrollment (day 0); * Prior use of UB-421; * Any acute febrile illness within 14 days before initial administration of UB-421; * Treatment with another investigational drug or other intervention within 28 days of Screening; * Any active malignancy that may require systemic chemotherapy or radiation therapy; * History or other clinical evidence of: * Significant or unstable cardiac or cerebrovascular disease (e.g., angina, congestive heart failure, recent stroke or myocardial infarction); * Severe illness, malignancy, immunodeficiency other than HIV, or any other condition that, in the opinion of the investigator, would make the subject unsuitable for the study; * Active drug or alcohol use or any other pattern of behavior that, in the opinion of the investigator, would interfere with adherence to study requirements; * Systemic immunosuppressive medications received within 3 months prior to enrollment (Exceptions: \[1\] corticosteroid nasal spray or inhaler; \[2\] topical corticosteroids for mild, uncomplicated dermatitis; or \[3\] oral/parenteral corticosteroids administered for nonchronic conditions not expected to recur \[length of therapy \<=14 days, with completion in \>=30 days prior to enrollment\]); -Any radiation therapy within 4 weeks prior to Screening.