How to Make many pizzas for large party?

Yes, preparing discs of dough ahead of time, separated by parchment, wax paper or clingfilm does work. The biggest risk is that the dough tends to dry out a bit, so keeping the whole mass wrapped up in clingfilm and possibly in wide closable containers may be worthwhile.

I don't know how long it would take you to pre-portion 20 pizza doughs; I'm not super-efficient on that yet so it would probably take me a good solid hour. That might be short enough so as not to require additional retardation.

Most pizza joints at least pre-portion the balls of dough, and they let them relax at (oven-) room temperature, so that they're easy to stretch.

If this is a casual party with friends, rather than a formal dinner or a catering gig, though, you may consider involving your friends to do the work; they may appreciate the social aspect of throwing/rolling dough together (depending on your technique preference), and even topping the pizzas themselves, with your guidance. You may want to make a bit of extra dough to accommodate errors.

I've actually been to an event where everyone brought their own preferred dough recipe to test it out on a wood fired oven, which was a leisurely several-hour event with many successes and a few "failures" (or lessons learned; brioche dough doesn't love 700F ovens). We all just grabbed space on the bench when it was practical, and queued up for the oven when practical.

An alternate strategy is to have plenty of dishes out on the table that aren't time and temperature sensitive, and let people nibble casually while you prep. Marinated vegetables, cold cuts, cheeses, bean dishes, etc. Then spend time chatting with each person you're making pizzas for while you prep them, maybe three or four at a time, to tweak to their preferences and whims.

I've made 8-10 pizzas a few times for large parties at my house. Unless you have someone to help, you're not going to get to mingle much while you're baking. And even if you have someone to help, you'll need to really work well together and know who's keeping an eye on things and keeping the process moving.

It also depends on your desired pace. I've only done this at a party when everyone was basically ready to eat at once, so I was trying to bake as fast as possible. If your party spans a few hours and people will be sporadically coming and going and will want pizza at various times, it can obviously be more leisurely.

I like to use a very wet dough, so doing pre-stretching is just impossible, since it would stick to any surface it sits on (or anything covering it) if I tried to stretch it in advance. But if you have a more typical American-style drier dough, it is certainly possible to pre-shape and refrigerate. (As JasonTrue mentions, the biggest concern is to be sure the dough doesn't dry out excessively.) At a minimum, you want to have the dough divided and pre-shaped into small disks. If you don't already do this, to make the process more even, I would strongly recommend portioning the dough accurately, e.g., with a scale. That way you know exactly how big each pizza should be stretched, exactly how much cheese and sauce would be appropriate for that size, etc.

The other question is how much variety of toppings you are going to have. Obviously you want them all prepped and ready in advance, but are you doing to have people choose individualized toppings, or are you just going to make a few standard types? It's really critical to do portioning effectively in either case. For example, know exactly the right amount of sauce to use for your portioned dough, and have a measuring utensil ready so you can dish it out quickly and accurately. If you're using a standard set of cheese (or a couple cheese possibilities), either pre-portion it or have a scale standing ready and know exactly how much is appropriate for that size pizza. Etc.

The last time I did this (recently), I baked 8 pizzas in about 30-40 minutes by myself. I had the dough pre-portioned, though I had to stretch each piece before topping. I had all of the ingredients ready and scaled or measured them quickly to portion each pizza and maintain consistent quality.

Even with all that prep, though, I didn't have much time to talk to anyone while I was baking -- well, not until I slowed down for the last two pizzas, since people weren't eating quite as fast by that point.

Anyhow, my most important recommendation is to do a "trial run" of whatever method you think you're going to use in advance if possible, perhaps with only 3 or 4 pizzas or whatever. The last thing you need is to discover that your novel techniques (e.g., pre-shaping and refrigerated retarding) caused the dough to do something weird that interfered with the quality or caused delays.

4 times a year I bring a 2 or 3 portable pizza ovens (small propane powered) to my workplace and make pizza for our team. I make 20-30 depending on how long I'm going to have. Here is what I do

• Make the dough (which for me involves proofing at room temperature for an hour and then into the refrigerator until two days before I'll be cooking)
• Two days before I'll be baking the pizza, I ball all of the dough and put on 1/2 sheet pans and/or hotel pans and store in the refrigerator.
• The day before, I stretch out all but maybe 4 of the balls onto pizza pans. Then I put the undressed pizzas into pizza boxes (can buy online, from a local restaurant store, or local pizzeria) and put in the freezer.
• I bring the refrigerated dough and the frozen pizza blanks with me along with some extra pizza pans. Also the portioned toppings.
• Once I'm at the worksite, I'll stretch out the refrigerator dough and decorate. Then bake them. I take the frozen pizza blanks out of the boxes and put them on the counter to start warming (I have a 45 minute commute so they are starting to thaw already). While they bake (2 or 3 at a time) I am decorating the next batch.
• The pizza bakes for 4-5 minutes for the refrigerated dough and more like 5-6 for the cold, but not really frozen any longer, pizzas.
• The key is to have all of the ingredients premeasured. I used a measured flat bottom spoon for sauce, weigh out an put into small zipper bags the cheese and portion out other ingredients. I find it best to stick with no more than 2 sauces and 3 pizza options (I usually go with tomato sauce and garlic cream sauce for sauces, mozzarella and swiss cheeses. This lets me make cheese & pepperoni, cheese & sausage, & vegetable (garlic cream with vegetables) pizzas).
• It takes a 60 - 70 minutes to do about 30 pizzas (3 at a time). I don't think this would be doable if you needed to portion or grab from a larger bag of ingredients while you're trying to make the pizza. Portioning is key. Having pre-stretched pizza blanks is another critical time-saver.

You also need to work smartly. Pull out the cooked pizzas and start the next ones cooking before slicing those you just pulled out etc.

If freezing the pizza didn't work, I was going to try par-baking the pizzas. But freezing worked so well, I've not tried that. That may be another option.

Make your own frozen pizzas: http://www.thekitchn.com/how-to-make-homemade-frozen-pizza-cooking-lessons-from-the-kitchn-186527

Pizza is best completely fresh, but you might consider this frozen option - but you could alternatively refrigerate short term rather than freeze using the same method.