Stand them up. You'll to modify your shelves.
I got a plate rack and stand them up but they take up a lot of room that way. We have our smaller plates standing up sideways and it works much better and are easier to get to. Obviously we had them for 8 years now, so we found a solution, but it's still annoying and the new plates won't have that problem.
I should clarify that our "current" set is our old set, I just ordered the new ones, I don't have them yet.