Most students pay most/all costs for med and law school and masters degrees. There are some merit offers for high LSAT scores but usually those are for non-T17 law schools. There are merit offers for med school for high MCAT scores or for the small number who have multiple acceptances.
The PhD programs worth attending will provide funding.
What type of schools interest your daughter? Small? Large? Rah rah? Quiet? Greek systems?