While some car rental companies carry large vehicles, such as 10 and 12 passenger vans, they don't carry them at every location (not even close to every location!) and some company may only carry the vehicles seasonaly (ie. in the summer).
It would be very helpful if car rental company websites would simply list the locations where 10, 12 or even 15 passenger vans are available, but sadly they don't!
I don't know where you want to rent a van for 10 people, but I can give you a few websites to try. Just check for your preferred location, with your expected dates and times to see what vehicle options are available. If a 10 or 12 passenger van does not show up, it basically means that in that particular town/city, that vehicle is either not available for those dates, or more likely not available because they simply don't carry it in their fleet.
(car rental company links open in new windows)
You might try:
15-passenger vans are available in select Rent-A-Wreck rent a car locations.
you can check Rent a Wreck Location Guide
to see if there is a location where you want to rent.
Hope this helps!
Pages from this site, relating to this topic:
The Basics of Car Rental
Making Car Rental Reservations
Vehicle Guide Specialty