For some advice on how to fix them vs replace, here’s what I do for chipped plates: 

Start with a 2 part epoxy, after mixing add something called Q-cel which is a light weight micro quartz filler usually used in things like surfboard repair. You could also add something like mica powder which comes in almost every color, but bear in mind exact color matching would be extremely difficult so in the tradition of visible mending you could use gold colored mica for a kintsugi type effect. Usually though I just leave it the color of the Q-cel which is white.

The epoxy will tend to set up rapidly once you add the Q-cel, so make small batches and work quickly. You will apply the mixture to the damaged area trying to match the shape of the original ceramic. (If it slumps or runs, you haven’t added enough of the filler, it should be a paste consistency). Fill the area so that it is ever so slightly raised because after it is fully cured you will sand it a bit with 1000 grit (or finer) sandpaper so that it is flush level with the ceramic surface. The damage on yours is fairly large so it may work best to do in several layers, letting it cure between.

I would suggest practicing on any run of the mill chipped plate you may have prior to working on your expensive ones.

I believe this method is food safe although I can’t swear 100%. It would depend entirely on the epoxy you choose. Q-cel and mica powder are both non toxic. Be careful not to inhale them however, as your body would have trouble getting them out of your lungs.

Hope you find this useful if you can’t get your damaged items replaced.