The main issue in preparing a party is adequate planning. With careful planning you can handle a party as large as 25 in a standard kitchen (for more than that number you run into issues of stove top burners, oven space, counter space, serving equipment, refrigerator space, cooking equipment, and just plain space in general). Although you can rent equipment — including ovens and stoves — you still have the issue of finding a place to stage the cooking equipment. But with careful planning, well in advance, you can manage even larger parties.
I've been catering dinner parties for several years and I've learned a lot in that time and developed a couple of key tools - spreadsheets. I find these a huge help. But whatever the party's size, the key to success is detailed planning. This requires several passes, with each pass becoming more refined.