Is it possible to negotiate financial aid even in Early Decision?

[1NJParent]

@genghispekhan

The FA offer was a little over a week ago; we also already submitted the housing and enrollment deposit.

Your defintion of T10 may be somewhat different, but the colleges with ED programs that may have a claim to be T10 are Columbia, UPenn, UChicago, and Duke. Does any of these schools require enrollment and even housing deposits this early?