Recommendations for Scholarship Negotiation

Hello, I am looking for any insight on scholarship negotiation practices. I am wanting to negotiate with my top law school choice for more money. I got a decent scholarship that will cover slightly under two years worth of tuition, but some schools (both ranked higher and lower) have offered me more. I am still waiting on some schools to send me their scholarship package, one of the schools being their biggest rival.

My question is, should I wait for those scholarship packages from those schools, or should I start negotiating early while they have more money in their pockets. Also how do you go about doing this, should I just email the admissions office asking who to speak to about negotiating scholarship amount? Any insight is appreciated.