Sam,
My three best friends and I did that after graduation - it was awesome!
I am now trying to plan a trip for my whole extended family - only 12 people though

I know they (Disney) can help you with this - if you call them, they can tell you all the things they can plan with your big group.
Here's what I've done:
Checked prices of : 4 rooms at the All Star vs. a suite at Saratoga Springs or one of the nicer hotels. Suites = not worth it. The four rooms are still cheaper when you compare them with the amount of sleeping space and the number of bathrooms. If I were you, I would go as SOON as you graduate so you're not competing with schools end of the year trips. We actually went winter break of our first year of college - totally empty parks, cheap hotels, it was great! (I'm assuming you're graduating from HS...if you're graduating from college, go at the end of May. It's SO dead even though it's Memorial Day. It's fantastic!)
IMO, get five rooms (4 people in each) at one of the All Stars or Pop next to eachother, get a couple with adjoining rooms if you can, and talk to your friends. Do some of you want to just lay at the pools? Do you ALL want to go to the parks the same amount of days? If so, book the hotel and tickets together. (As long as one of you puts down the the initial deposit, when you get to the hotel you all can pay seperately...or at least we did.)
If you all want to do different things, have everybody buy their tickets seperately. Granted, it's cheaper to buy them in bulk, but if there's the whole issue of payment, you may want to do it that way. (That's a lot of money to put on someone's credit card, so make sure everyone's on board before you do it or you might get stuck with some extra rooms or tickets.) Otherwise, online, you can pick whatever tickets you want...for ex. Five 6-day Park Hopper Passes, Two 4-day Park Hopper Passes with Water Park option....there's just tons of choices :~) Sorry if you knew all this already:wave:
And I'd still call Disney and ask them what they can do with a party of 20...I bet they have some great ideas!