Negotiate Better Terms for PhD Fellowship?

[nealolaen]

Hello everyone - a long time lurker here.

I am very fortunate to be accepted to two equally fantastic PhD programs. What I heard from current PhD students in other fields (political science, philosophy, etc.) at my college is that there are people who used a second or third offer as a leverage to negotiate better terms for their top PhD fellowship offer, such as a moving fund, extra summer stipend, or even, in one extreme case, one semester of teaching taken out of the stipend requirements. I am curious if leveraging funding or teaching requirements is also something common in the field of art history, and any warnings for possible negative outcomes or strategic suggestions on how to do it would be greatly appreciated.

Bt the way, I think the two advisors I applied for at each program know each other very well... I will probably end up working with both of them in the very near future. Thank you all very much!