How must Grovers algorithm be modified in order to solve 3-SAT?
Grover's algorithm is already suitable.  It promises that if there is at least one match, then it will output at least one match.  It doesn't promise to output all matches, but you don't need all matches.

It is usually described to work in the case where there is zero or one items that match, but that's just because those are the hardest cases.  If there are multiple matches, the algorithm will still work and will still find a match; and the running time will remain the same.