Using the 100 km Karman line as the barrier. The current record is 19, set in 2021
https://en.wikipedia.org/wiki/List_of_spaceflight_records#Human_spaceflight_firsts
This would not count any flights by Virgin Galactic as they do not go up to 100km.
There are currently 10 people in space as of April 12, 2024 (check the current number at https://whoisinspace.com/) and there is a scheduled Blue Origin space tourism flight, but that would only bring us to 16. To set a new record, we will probably need a confluence of an ISS or Tiangong crew change happening at the same time as a space tourism flight.
If Wikipedia records a new record for number of people in space (100km), this resolves to YES.
Perhaps worth noting:
https://www.space.com/human-spaceflight-record-20-people-in-space-2024
says record is 20 as of Jan. 26 2024 but this includes 6 on Virgin Galactic which don't count and it is also before this claim was created.
Outside of changeovers we would normally have
ISS via Dragon 4
ISS via Soyuz 3
China Tiangong space station 3
which is only 10, so 6 on New Shepherd only gets to 16.
If 6 on New Shepherd during Soyuz or CSS changover that only ties at 19.
If 6 on New Shepherd during normal dragon changeover that gets to 20.
New Shepherd during ISS and China space station changeovers would also do it but seems unlikely - next China Tiangong Space Station planned for ~Oct 25 while dragon planned for 25 Sept and Feb 2025.