Do any newer vehicles exist that are NOT SUVs, vans, or minivans that seat 7 or more people?

AnneMarie

You are making two mistakes, IMHO.

You are getting hung up on labels.
You are not dealing with reality if you think that something “small” will hold 7 (or more !??!) people.

The best bets, IMHO, would be the Toyota Sienna and the Honda Odyssey, but these vehicles are definitely BIG. Some SUVs would also serve the purpose, but probably would not have the total carrying capacity (passengers + cargo) that a van would have.