Requesting funding match after offer?

[Aminoacidalanine]

A clinical psychology program that has good research fit has offered me a spot. The problem is that they have lower than average funding that is only guaranteed for only 3 years (although I've been told that almost all students receive funding for 4 years). This is especially an issue for me because I am not a US citizen so I wouldn't be able eligible for external funding. I’ve been told that sometimes schools are willing to match their stipend when you have competitive offers, which I currently do. Is this something that is doable and if so how (and who) should I ask?

[Oshawott]

The "guaranteed for three years" thing is problematic, and I would question current students with regards to who has gotten funding in Year 4 (and also look at your POI's history, to see if their students have successfully gotten Year 4 funding, and from where).

As for the "lower than average funding", what is the cost of living like in the area? Some schools may offer much higher funding packages, but in effect, it is just to offset the higher cost-of-living, and I'm fairly certain that this will factor into stipend negotiations.