My frittatas always deflate. I've heard all kinds of differing advice: add flour, add tapioca flour/starch, add corn flour, add baking powder... I was once even told to add a little yoghurt! The base recipe I use calls for 6 eggs and 1/4 cup milk, and then some onions, garlic, and then a little of whatever vegetables are in the fridge chopped up fine... and then shredded cheese on top once it's already half done (but I don't think the cheese is so heavy that it's causing the whole thing to collapse and deflate - I really only use a sprinkling). What's the best way to keep a frittata from deflating?
You may want to see Serious Eats' coverage of scrambled eggs.
Getting them to puff initially requires a little higher heat. Adding extra liquid (water, milk, cream) will result in softer eggs, so you may want to reduce or eliminate it.
As for the cheese -- it really depends on how much you're adding. If it's so thick you can't see the eggs under them, I'd recommend either reducing it so it's a bare sprinkling, or mixing some in with the eggs and then only a small bit on top.
For a fritata specifically, you should be careful about not overcooking it -- it can cause it to deflate if the air bubbles over-expand and burst.
When dealing with serving frittatas at room temperature or chilled, make sure that you let it cool slowly -- you need to make sure that the proteins get a chance to set up before the air bubbles shrink significantly.
A frittata is always going to deflate some after you take it out of the oven, you cannot prevent that. Air and the moisture in the egg expands as they heat, causing the frittata to grow. While it is grown in size the egg hardens, trapping the expanded gasses and stabilizing the structure. When removed from the oven the air cools and contracts, and as eggs have a slightly elastic nature when cooked the structure of the cooked frittata will shrink some. The same forces cause some of the rise in cakes, however flour and sugar form a more crystalline structure which holds shape better, so in general shrink less when cooled. I expect to lose maybe 1/3 of the height of the frittata after its cooled, it's just the nature of the beast.
As for additives I usually add some combination of of milk or cream, herbs, spices, meat, vegetables or cheese and as long as you keep the proportions reasonable it doesn't seem to impact the expansion of the egg much.