Sick to my stomach

Sorry, I should clarify. I'm attempting to proceed to a Ph.D. post-J.D., and for law schools, if you get multiple offers, you can bootstrap your way up the rankings - in other words, if a lower-ranked school gives you more generous funding, a higher-ranked school won't necessarily match, but might sweeten the pot. While this doesn't work in every case - Yale Law School is not going to be impressed by your offer from anywhere but Harvard, and if you try and pull this on them with a Harvard offer, they'll tell you to go to Harvard - it can work a little further down the rankings. So here's my hypo, fully fleshed out (and if you know the programs to which I'm applying, you'll know which ones I'm referring to). Program A is not as highly ranked as Program B or C, but is up-and-coming and is well-known for being very generous. So, if I get offers from both Program A and Program B or C, what is the likelihood that I could shake extra support from B or C? Or could I use this to pull myself off a waitlist? Or is the dynamic just too different?

So...let's play hypothetical. Please don't fight the hypo. Let's suppose one got multiple offers with varying levels of support. How could one leverage those multiple offers into more support from a program you really wanted to join, but which was not as generous in its support? Note that at the moment this is nothing more than a thought exercise - I don't have even one offer. But hope springs eternal, and I'd like to be prepared to have that wonderful problem.