Starwood and Marriott owners both have first priority for any deposit from their own system in II, so it may be difficult. Your best bet is to put in a very wide request.
The most successful strategy for a II exchange includes:
1) Put in an on-going request as early as possible (12 or more mos. out) so it's in place BEFORE the deposits are made, and ahead of other exchangers.
2) Request a wide-range of weeks.
3) Request as many resorts as possible
4) Even though the online inventory is the leftovers, sometimes gems pop up, so it's worthwhile to keep checking it, even when you have an on-going request in place. If you see something you want, you can still grab it online, which will automatically cancel your on-going request.
5) If you need a specific check-in day, you must call II after putting in your request online and specify the day of the week. Otherwise, your on-going request automatically defaults to Thursday, so your check-in day could be Thurs., Fri., Sat., or Sun.
Strategies that will decrease your chances of getting a trade:
1) Only requesting school holidays
2) Only requesting one specific week
3) Only requesting the very top resort in an area (which you may not have the trading power for)