We often grill sandwiches without cheese --- I usually use the more artisan breads - country, sourdough, etc. (I guess some of them would be hard to cut to fit the sandwich machine) - I like to spread pesto thinly on the bread, top with roasted veggies (usually peppers, eggplant, onions); and then (in season) thin slices of tomato) - spread outside with butter - and grill.

What about egg with ham - thin slice of ham on the bread - an egg (either just out of shell - or lightly whisked); another slice of deli ham - then top of bread. Since its 'liquidie' - it is best to butter the sides of the bread first - in fact, I usually put it on the grill before I put the egg on - and then work quick!
Peanut butter and jelly - add some sliced banana or whatever you like.

Have you tried the 'desserts' some often make in the sandwich makers? White bread with a scoop of canned pie filling in center; topped with 2nd slice of bread. Sprinkle with confectioner's sugar after removing. My kids used to like the bread spread lightly with peanut butter; then some chocolate chips and mini marshmallows scattered atop; top bread ... and they'd eat it with ice cream!

What about leftovers - roast beef with a wee amount of gravy and some leftover onion or carrots? Or bbq or sloppy joes or chili -- tho in those instances it has to be thicker texture and you can't put too much in.

We always took our grill to the shore with us - and it really got a lot of use. leftover chicken; the only way my kids liked canned tuna - was (oops - forgot!) when I put shredded or small diced Monterey Jack cheese in it - and made sandwiches with it on the grill. I've never tried it without cheese. Sorry about that one!

I would think just about anything .....
Enjoy!