I would like to replace a drop in stove top with a larger unit and need to enlarge the opening
Can I do rhis by using a router,do I need a special bit to cut the Corian?

Treat Corian like a hardwood. A router can do the job but its best to finish the cut and clean it up with a router. You can cut it with a medium tooth saw or jig saw also. Put tape down on the top surface so your saw doesn't scratch any part that will show. Clamp or hot glue a straight edge on the surface as a router fence.\, the hot glue can be popped off later.

There are three other things you need to do.

1. Even if you use a router to cut or clean up make sure that you sand out all toothemarks with 220 grit sand paper.
2. Make sure that you leave sharp inside corners. make sure all corners are radiused.
3. Use an aluminum tape, on the edge, to reflect and disburse any heat.

I hope this helps
Ken