I need to enlarge a cooktop cutout in my existing corian approximately 1/2 inch on both sides. I can't use a router because the backspash is too close. What else can I use-roto-zip, dremel? Thank you

The roto-zip may work, they make several different types of bits for the roto. You might have room for a jig saw.

You can use a Roto-zip but replace the standard bit with a solid carbide upspiral end mill if you can. Cut slowly (about 30 inches per minute).

Clamp or hot melt glue down a fence so that you keep the line straight. (If you wish to use hot melt glue, apply the glue to the wooden fence first then press it onto the Corian. Remove by taping or prying it off the Corian.)

Use a shop vacuum as you work to suck up the shavings and dust, as it will fly everywhere.

After you cut make sure that you sand with 220 grit sandpaper to remove any tooth marks as they will be stress risers, that will be a place for a crack to start. The area around a cook top is subject to many heating and cooling cycles and this is a stressor of Corian. Also make sure that you replace the insulating tape that should be around the opening. DuPont recommends their Nomex brand.

The carbide segment saw blade of the FeinMultimaster might work. C. & E. FEIN GmbH - Der FEIN MULTIMASTER

I have both, bit no corian to try it on, The unit oscillates rather than rotates to cut.
Note you can cut a square edge. If I had a scrap of Corian, I might be willing to try it for you. A friend MIGHT have some.

It is a wonderful tool but nothing that "fein" is necessary. The roto-zip or an all-purpose blade on a jigsaw will work well and probaby a little faster.