Broadly Neutralizing Antibodies 3BNC117-LS & 10-1074-LS to Prevent Relapse During ATI

Step 0 Inclusion Criteria: 1. Ability and willingness of participant to provide informed consent to enter the Screening and Pre-Entry segment of the study. 2. Individuals age ≥18 to ≤70 years. 3. Weight greater than or equal to 50 kg (110 pounds) and less than or equal to 115 kg (253.5 pounds). 4. Documented HIV-1 infection. 5. For participants who can become pregnant, a negative pregnancy test at Screening must be obtained. 6. For participants who can become pregnant, participant must agree to use two methods of contraception. 7. Participants who can impregnate a partner and who are engaging in sexual activity that could lead to pregnancy must agree to use condoms from 10 days prior to the first dose of study drugs, while receiving the study drugs, and for 12 months after the last dose of study drug to avoid impregnating a partner who can get pregnant. 8. Willingness to use barrier protection (male or female) during sexual activity. Step 0 Exclusion Criteria: 1\. Currently breastfeeding or pregnancy. Step 1 Inclusion Criteria: 1. On stable suppressive Antiretroviral Therapy (ART) for at least 48 weeks prior to Step 1 study entry with no interruption of ART for 7 consecutive days or longer in the 48 weeks prior to entry in Step 1. 2. If on an NNRTI-based regimen, willing to switch to an integrase inhibitor-based regimen at least 4 weeks prior to discontinuing ART. 3. CD4+ cell count \>450 cells/µL obtained within 90 days prior to study Step 1 entry at any US laboratory that has a Clinical Laboratory Improvement Amendments (CLIA) certification or its equivalent. 4. CD4+ cell % ≥15% obtained within 90 days prior to study Step 1 entry at any US laboratory that has a Clinical Laboratory Improvement Amendments (CLIA) certification or its equivalent. 5. Nadir CD4+ cell count ≥200 cells/µL. (NOTE: If documentation is not available, then participant recall is acceptable.) 6. Plasma HIV-1 RNA levels of \<50 copies/mL for at least 48 weeks prior to Step 1 entry at any US laboratory that has a Clinical Laboratory Improvement Amendments (CLIA) certification or its equivalent (NOTE: At least two viral load measurements within 48 weeks prior to the Step 0 screening visit must be available for review. A single plasma HIV-1 RNA \>50 copies/mL but \<200 copies/mL that is followed by an HIV-1 RNA \<50 copies/mL is permitted.) 7. 3BNC117-LS IC90 less than 1 mcg/mL and MPI \>98% in PBMCs or plasma with the Monogram PhenoSense assay. (NOTE: Monogram PhenoSense assay obtained for eligibility to other clinical trials may be used for eligibility.) 8. 10-1074-LS IC90 less than 1 mcg/mL and MPI \>98% in PBMCs or plasma with the Monogram PhenoSense assay. (NOTE: Monogram PhenoSense assay obtained for eligibility to other clinical trials may be used for eligibility.) 9. The following laboratory values obtained within 90 days prior to Step 1 entry by any US laboratory that has a CLIA certification or its equivalent: 1. absolute neutrophil count (ANC) ˃1,000/mm3 2. hemoglobin \>10 g/dL 3. platelet count ˃100,000/mm3 4. eGFR ≥60 mL/min/1.73m2 5. AST (SGOT), ALT (SGPT), and total bilirubin \<1.5 x ULN 6. alkaline phosphatase less than 1.5 x ULN 10. Completion of pre-entry leukapheresis with documentation of at least 1 billion cells of stored PBMC (e.g., ≥20 aliquots of 50,000,000 PBMC). Sites must receive confirmation from the processing lab via phone, email, or fax that specimens have been entered into the ACTG's Laboratory Data Management System (LDMS). 11. For participants who can become pregnant, a negative pregnancy test at Screening must be obtained. Step 1 Exclusion Criteria: 1. History of AIDS-defining illness within 36 months prior to study Step 1 entry 2. Any clinically significant acute or chronic medical condition (such as autoimmune diseases or active tuberculosis), other than HIV infection, that in the opinion of the investigator would preclude participation. 3. Any history of an HIV-associated malignancy, including Kaposi's sarcoma, or any type of lymphoma or virus-associated cancers. 4. History of Progressive Multifocal Leukoencephalopathy (PML). 5. Active or recent non-HIV-associated malignancy requiring systemic chemotherapy or surgery within 36 months prior to Step 1 study entry or for whom such therapies are expected in the subsequent 12 months. (NOTE: Minor surgical removal of localized skin cancers (squamous cell carcinoma, basal cell carcinoma) is not exclusionary.) 6. Receipt of cabotegravir-LA IM or rilpivirine-LA IM within 24 months prior to Step 1 study entry. 7. Known resistance to all drugs within two or more ARV drug classes. (NOTE: M184V/I is an exception, and should not be considered when assessing this criterion. Prior HIV resistance testing is not required.) 8. History of systemic corticosteroids (long-term use), immunosuppressive anti-cancer or other immunosuppressive agents, interleukins, systemic interferons, systemic chemotherapy, or other medications considered significant by the investigator within the 24 weeks prior to Step 1 study entry. 9. ART initiated during acute infection (defined as p24, HIV NAAT, or HIV RNA PCR positive, and negative or indeterminate HIV antibody testing). 10. Any history of receipt of therapeutic HIV vaccine or HIV monoclonal antibody therapy. 11. Participation in any clinical study of an investigational product within 12 weeks prior to Step 1 study entry or expected participation in such a study during this study. 12. Hepatitis B or C infection as indicated by the presence of Hepatitis B surface antigen (HBsAg) or hepatitis C virus RNA (HCV-RNA) in blood. 13. Known allergy/sensitivity or any hypersensitivity to components of either study agent or their formulation. 14. History of or current clinical atherosclerotic cardiovascular disease (ASCVD), as defined by 2013 ACC/AHA guidelines, including a previous diagnosis of any of the following: 1. Acute myocardial infarction 2. Acute coronary syndromes 3. Stable or unstable angina 4. Coronary or other arterial revascularization 5. Stroke 6. Transient ischemic attack 7. Peripheral arterial disease presumed to be of atherosclerotic origin 15. 10-year ASCVD risk score estimated by Pooled Cohort Equations \>20% in participants ≥40 and ≤ 70 years of age. 16. Diagnosis of cirrhosis 17. Diagnosis of untreated syphilis, gonorrhea, or chlamydia. (NOTE: Candidates who began treatment for any of the above are not excluded.) Step 2 Inclusion Criteria: * Willingness to continue the analytical treatment interruption (ATI) and be monitored. Step 2 Exclusion Criteria: * None. Step 3 Inclusion Criteria: * Meet ONE of the following: 1. Meeting one or more ART restart criteria as defined in the study protocol 2. Despite completing 72 weeks of ATI without meeting one or more ART restart criteria, declines participation in A5385, or is unable to enter A5385. Step 3 Exclusion Criteria: * None.