We call it "scholarships". Is that the same thing you're talking about with "sponsorship"? For better or worse, we have been setting up the form so that the base price is the full amount and then adding promotion codes that may be FULSCH for full scholarship or HLFSCH for half scholarship, etc. We'll include instructions before the question so the person knows (provided they read it) to enter the promotion code at the bottom of the form before going to check-out. We ask the question: "Do you need a scholarship?" and then the answers could be anything like "I can pay 50% (HLFSCH)" or "I will need a half scholarship (HLFSCH)" or something like that and then putting the promo code in parenthesis after it so they remember (and know the promo code). We'll also have another question that says something like "I would like to contribute toward the scholarship fund" or something like that and associate prices to the specific answers so it charges them an additional amount accordingly. You could also (if you want to keep it straight, though we don't) have a question about who the scholarship is designated for and have them fill in the blank with a "undesignated" as the default answer. The only problem with this system is when someone wants to contribute a certain amount that's different than what you have created. The last retreat we did we had a full, 3/4, half, 1/4 scholarships as well as a $20 donation as options to pay additional to the retreat price, and then had full, 3/4, half, and 1/4 scholarships that people could choose from if they needed one.
A good report that I've found to like is M6023. You'll see the Adjustment column in Sheet 1 to show all your scholarships (and whatever else you may use it for) and on Sheet 2 who actually paid for what in the adjustment column. We've then been giving that info to our financial department who switched their payment to a contribution designation. (Too bad you can't choose different accounts for the payment info when creating the form. That would be handy for payment vs. contribution predicaments.)