* Update to sections 6.7.1.D and 10 (plus tables 1 & 2) to further clarify sub-study procedures in countries other than UK and Italy * Trial summary updated with further details of treatment groups and distribution of active treatment and placebo. * Details on randomisation stages added to Trial summary and section 3.4. * Minor change to section 11.2: Word “component” was replaced by “approach”. * A number of typos across the document were corrected.

* Exclusion criteria updated to include personal and/or family history (parents and siblings) of clinical autoimmune disease or reactive arthritis * Sections 6.2, 6.4.1 and 6.7.1: Microbiome analysis will be done if the participant is willing and able to produce a stool sample, and the laboratory local to the clinic is able to process and store the sample at -80°C within 4 hours of the sample being produced. * Sections 6.2 and 10: Participants from France, Germany, Spain and Switzerland will be invited to take part in substudies, provided the local laboratories pass the quality control checks for sample processing and storage.

* Section 5.6 Protocol treatment discontinuation: Participants who have received at least one injection or infusion will be asked to remain in the trial for the purpose of follow-up and data analysis at least until week 24 or for 4 weeks after the last trial intervention, whichever is the longest. * Section 5.10 Non-Trial Treatment: Participants will continue on their combination antiretroviral therapy through to week 24 when they will interrupt treatment provided it is safe to do so. Pregnancy added to the list of circumstances that may lead to resume cART. * Section 6.3.9 expanded. * Sections 6.4, 6.5 and 7.2.1: Notable events such as pregnancy may lead the Trial Safety Group to conclude that: * ART interruption is inadvisable * ART should be resumed * Interventional products will be discontinued * Section 6.7.1F Microbiome Study: Only sites where samples can be processed and stored at -80°C within 24 hours from being produced will participate and from participants who are willing and able to follow the procedures for collection. Exclusion of participants with chronic diarrhoea. * Section 7.2.1 Pregnancy: All pregnancies, including those occurring in female partners will be followed up to collect information about the outcome. * Section 8.1: Risks of exacerbation of recognised adverse events due to the combination of vaccines and vedolizumab and occurrence of new adverse events; Risk of disease progression following cART interruption and occurrence of progressive multifocal leukoencephalopathy (PML). * Sections 9.2 and 9.3 were created to describe the phase I and II components respectively. * Section 9.5 Interim Efficacy Stage: Changes made to “Time to interim analysis” and “Duration of the whole trial”. * Sections 9.6 and 11.2.1 Ethical Considerations: IDMC will review the cumulative safety data after the 12th participant has had their first safety visit at week 1 or 4, before expanding recruitment. * Section 10 Ancillary/Substudies: clarification

* Treatment(cART) will be resumed when CD4 T-cell count falls to ≤350cells/mm^3 confirmed * Introduction updated with more recent data on the global AIDS epidemic and updated information regarding cART benefit and toxicity. * Introduction and Risk Assessment updated with recent case of PML in HIV-positive individual. * Introduction updated with reference to a recent study of vedolizumab in HIV-positive individuals. * Table 5 footnote and 5.4.4 updated to clarify vaccine and infusion visit schedule. * Wording in 5.2.3 amended to be clear on what participants randomised to placebo should receive. * In 5.6 detailing protocol treatment discontinuation, one point regarding toxicity or adverse events has been reworded for clarity and a further point added about restarting cART. * An additional section was added to detail additional and more frequent pregnancy testing for women of childbearing potential throughout the trial. * 6.3.3 and 6.3.6 updated to include checklist of neurological symptoms associated with PML. * The procedures detailed in 6.5 now indicate that an Adverse Event assessment will take place at every follow-up visit. This section also adds that cART should be restarted in the case of pregnancy in a female participant, updates have been added to the wording around notable events and expedited reporting. * 10,000 copies/ml or more HIV RNA has been removed as a Notable Event from the list in 7.2. * The list of Notable Events now includes pregnancy. * 9.1 has been updated to explain that the randomisation of the first 12 participants will be restricted to chronic infection stratum. Clarification was also made in this section on the ratio between the four randomisation arms. * 9.5, Interim Safety Stage, has been added to detail a safety review to be performed when the 12th participant has their first safety visit following administration of product. * Table 9 has been updated. * A deletion was made to 9.8 with regard to primary outcome analysis.

* Inclusion criteria - the CD4 T cell count at screening has been changed from > 600 cells/mm^3 to > 500 cells/mm^3 (trial summary and section 3.1 updated with this information). * Trial Assessment Schedule for Site Investigators (Table 1) - the visit windows have been updated to ±3 days for the early, more frequent visits, and a visit window of 0 days has been given where visits must occur according to the individual visit schedule. The footnote of Table 1 has also been amended accordingly. * In section 5.4.5 an error was corrected which referred to the MVA vaccine (or its placebo) being given at the same visit as an infusion (this will only be the DNA vaccine or its placebo). * SAE and Notable Event reporting has been clarified throughout in the text and in the blue boxes. SAEs, Notable Events and Pregnancy must be reported within 24 hours of the investigator becoming aware of the event. * Section 18 (Appendices) was updated to refer to the ‘Participant’ (rather than ‘Patient’) Information Sheets to match the appended documents.