As noted, Marriott exchanges go thru Interval International. But Marriott deposits are held exclusively for other Marriott owners for a period (30 days?) before being available to other non-Marriott exchangers.
There is also the Marriott Florida club, which includes 5 properties (Miami, Ft Lauderdale, Palm Beach, Orlando-Grande Vista, and Panama City). If you own one of these, you can reserve into any of the others without going thru II.