This will be a big change, and space IS the issue. It is more feed, more water, more eggs, more manure and bedding. And disposing of eggs, manure, and dirty bedding. In the summer, this could be a real problem.
Personally, if you are a farm setting, that is totally different than a backyard set up of 3 hens. I would not recommend 20 birds in a truly backyard setting. And to be honest, I would never take birds that I feel sorry for.
When you go to get the birds, do an in-depth inspection of their feathers looking for parasites. DO NOT take if anything has a nasal discharge, or sick and lethargic.
I am a believer in a coop, but also shelter in the run that offers protection from the wind and some shade. My run is full of perches, roosts, platforms that bird can get under or on top of, hideouts with pallets leaned against a wall. This allows birds to get away from each other and makes for a happier flock. Multiple feeders is a good idea. I generally use two for 12 birds, add a third when adding younger birds. I have never had any problem just having one waterer, but others have recommended it. My run is covered across the top with fencing.
You may wind up with one or two birds that just do not adjust to new flock. It might be that your set up, (even if it measure correctly) does not work for that head count. Be willing to remove some birds until you get a happy flock. Not all birds will work together, and wishing they would all get along, won't work.
Just curious, what are you going to do for coop and run? Obviously what works for 3 birds will not anywhere close to be enough for 20 birds.
Mrs K