Can anyone who has successfully negotiated an increased offer speak to when in the process they made their request? For example, in my position, I have multiple offers, some better than others, but all from great schools (SIPA, SAIS, Fletcher, etc.), any of which I think I'd jump at if they offered me a full ride (my best offer is 2/3 tuition at this point). My current plan is to visit all the schools during their admitted students' days over the next few weeks, and then after I really have a feel for which programs/places I truly prefer among my 5 options, reach out to the top 1-2 and ask for more funding. My parents think this is the right approach, as it will allow me to more honestly tell the schools that after visiting that they are my top options. The idea is that once the schools know that they are truly my top option, with funding as the only obstacle, they might be more generous/open to granting me more funding.
On the other hand, I could reach out right now to all of them asking for more funding, to match the 2/3 offer, but not necessarily indicating to them they are my top choice (I could also tell all of them they are my top choice but at first glance, that would seem a bit disingenuous. Although it is true to the extent that if any of the programs offered my a full ride they would immediately become my top choice.). The reason to do this would be if I thought that the schools might have a smaller pool of funding to draw from if I make my request in 3 weeks compared to making the request now.
Any thoughts?