Xothebijooubox on Instagram has done this with her Milan setting. She puts a plate below the stone like a foil, but with a gap for cleaning. It is quite clever. I don’t know how it would do in real life.
I have a rose cut and I put aluminum foil under it the other day just for fun and I honestly like it better without. It truly changes the look and makes it almost pearlescent.
I'm wondering if a cup would be hard to clean because if it's not solid you will be able to see that through the diamond, but I'm no expert either.
You might want to try seeing what it looks like without any backing, I just got my first rosie and it is not backed. Thought I wouldn't care for a diamond you can see through but I actually enjoy it very much.
@Dee*Jay’s EC (it has an open cutlet and she preferred not to see skin) has a plate under the stone. Same idea as @JPie’s, just a different stone shape! It’s a clever design - you get the look of a plate without the cleaning hindrances