I have two internships in the US that are 16 weeks each. The first one is from early May to the last week of August. The second one is from the first week of September to late December. There is a period of five business days (plus four days in the weekend) between the two internships.
As someone who is not a citizen of the US, I'll be obtaining J-1 visas. It appears I can't combine the two visas into one 8-month long visa since the two companies and J-1 visa sponsors are different. As a result, I'd need two separate visas.
Would I be required to leave the country and enter again to get the new visa? How would the process work? It is very likely my first visa's expiry date would overlap with my second internship, so would I be allowed to stay in the US since I'd always have a valid visa (although it would switch in between the two internships)?