A Study of 2 Different Regimens of Tetravalent Ad26.Mos4.HIV Prime Followed by Boost With Modified Vaccinia Ankara (MVA)-Mosaic OR Ad26.Mos4.HIV Plus a Combination of Mosaic and Clade C gp140 Protein in Human Immunodeficiency Virus (HIV) Type 1 Infected Adults on Suppressive Antiretroviral Treatment

Inclusion Criteria: * Each participant must have documented Human immunodeficiency virus type1 (HIV-1) infection * Each participant must be on suppressive antiretroviral treatment (ART) for at least 48 weeks prior to randomization and on stable suppressive ART for at least 4 weeks prior to screening. Changes in antiretrovirals (ARVs) can be made for safety/tolerability reasons only until 4 weeks prior to screening * Each participant must have started ART outside of the acute or early phase of infection * Each participant must have a plasma HIV ribonucleic acid (RNA) less than (\<) 50 copies/ milliliter (mL) at screening and at least one documented evidence of plasma HIV RNA \<50 copies/mL after the last ART change. In case of ART change within the 48 weeks prior randomization, at least one additional more recent documented plasma HIV RNA \<50 copies/mL is required. One blip of HIV RNA greater than (\>)50 and \<200 copies/mL within 24 weeks prior to screening is acceptable, provided that the 2 most recent (after last ART change, tested before and/or during screening) HIV RNA results are \<50 copies/mL * Each participant must be medically stable as confirmed by medical history, physical examination, vital signs, 12-lead electrocardiogram (ECG), and clinical laboratory tests performed at screening Exclusion Criteria: * Anyone who is pregnant, breastfeeding, or planning to become pregnant while enrolled in this study, or within 3 months after the last vaccination * Anyone with contraindication to intramuscular injections and blood draws example, bleeding disorders * Anyone with acute illness (this does not include minor illnesses such as diarrhea or mild upper respiratory tract infection) or temperature greater than or equal to (\>=) 38.0ºC (degree centigrade) within 24 hours prior to the first dose of study vaccine; enrollment at a later date is permitted * Anyone with a history of malignancy within 5 years before screening (exceptions are squamous and basal cell carcinomas of the skin and carcinoma in situ of the cervix, or malignancy, which is considered cured with minimal risk of recurrence) * Anyone with a history of an underlying clinically significant acute or uncontrolled chronic medical condition or physical examination findings for which, in the opinion of the investigator, participation would not be in the best interest of the participant (example, compromise the well-being) or that could prevent, limit, or confound the protocol-specified assessments * Anyone with a history of Acquired Immunodeficiency Syndrome (AIDS)-defining illness according to Centers for Disease Control and prevention (CDC) criteria based on available medical history and assessed by the investigator as clinically relevant. A case summary for every participant with AIDS-defining illnesses assessed by the investigator as clinically irrelevant must be provided to the sponsor and Protocol Safety Review Team (PSRT), who will determine eligibility on a case-by-case basis prior to randomization * Anyone with a history of CD4+ less than (\<) 200 cells per millimeter cube (cells/mm\^3), based on available medical history and assessed by the investigator as clinically relevant. A case summary for every participant with history of CD4+ \<200 cells/mm\^3 assessed by the investigator as clinically irrelevant must be provided to the sponsor and PSRT, who will determine eligibility on a case-by-case basis prior to randomization * Anyone with chronic active hepatitis B (measured by hepatitis B surface antigen test) or active hepatitis C (measured by hepatitis C virus \[HCV\] antibody test; if positive, HCV RNA polymerase chain reaction test will be used to confirm active versus past HCV infection) or syphilis infection that has not been effectively treated. Positive syphilis serology due to past effectively treated infection is not exclusionary * Anyone who received or plans to receive: a) licensed live attenuated vaccines within 28 days before or after planned administration of any of the study vaccinations; b) other licensed (not live) vaccines - within 14 days before or after planned administration of any of the study vaccinations * Anyone who received an investigational drug or used an invasive investigational medical device within 30 days or received an investigational vaccine within 6 months before the planned administration of the first dose of study vaccine. Receipt of prophylactic or therapeutic HIV vaccine candidate at any time is always exclusionary. Exceptions: Participants can be included where the vaccine received was subsequently licensed. Participants with proof of having received only a placebo vaccine can also be included