each school has their own criteria and policies. However, no school that I know of lets you double dip and keep cash (other than federal pell grant)
teams look to maximize their athletic aid becuase it is so limited.
and the term "full ride" is thrown around too often and not clearly defined. is a full ride for academics full tuition, or does it include room and board, what about book?
The bottom line is the bottom line. What do you have to PAY?
But I can't think of a coach who is going to tell someone to turn down academic money and replace it with athletic money.
Let's say for instance you have a super star kid that runs 4:01 in the mile. Obviously he is a "full athletic scholarship talent." But if he has a 4.0 and a 32 ACT, then some school may pay for his full tuition with an academic award. The coach could then cover room board and books. SO HE PAYS ZERO. But he isn't on a full athletic scholarship. He may only count as .30, to .50 of a scholarship from an athletic standpoint.
There really is no SINGLE answer. Just speak with the coaches and the universities.