I have a 28" x 19" drop in sink and want to replace it without changing cabnetry or countertop. What options do I have to close the large hole. I know I can't match the white corian countertop, but I was thinking to put in some design of sorts to sit the top mounted sink.
Depending on how fussy you are about "matching" you can probably get quite close from a Corian contractor, if that's the actual product. Cut the hole bigger to where there's support (or add support) and join in a new section with the proper glues.
Logical alternative - when you can't match it, make it a feature - cut out the section to where there is support, insert a segment of black (or whatever color you like) solid surface countertop (assuming you want that aspect consistent) and put the new sinkhole in that.
3rd alternative makes it even more of a feature - leave the existing countertop alone, bevel the edges of a new sheet of solid surface and put it on top, rasing the sink 1/2" or so. Looks nice at my credit union, (without a sink) I don't know how it would fly in my kitchen long-term (might depend on whether you use a dish-rack to the side of the sink that would have trouble draining over that extra height.) You could make it larger to accomodate the dish-rack, though.
4th Alternative if the plumbing allows (down can be harder than up, depending on where the drain itself is vertically) would be to undermount a section of solid surface and cut out larger/bevel the edges of the existing sink hole. That limits the area you can lower to the space available in the sink cabinet with adequate gluing area to the underside of the top, while the overlay approach can be as large as you like.