Something so simple.

You could try a search for formal dining in your area. Is that what you mean by catered (since you mention doing this at a restaurant)? You can call the restaurants for details to see if they match your goals -- serving 3 course meals. I'm not sure where ATX is -- maybe Austin Texas?

For that many people you're probably looking at wanting to reserve a private room so look for restaurants in the area that have those. From there I think you'll probably just want to call and get in touch with their catering manager to be able to discuss needs, pricing, and reservations.

I think most restaurants will have appetizer, entree, dessert as 3-course options. You can request a meeting and tour with the manager to book a private room and discuss the menu. On day of, the server will go to each guest and write down all course selections at the beginning. The server and kitchen will coordinate timing. You could also opt for family style appetizers where platters would be placed on the table and guests serve themselves. They would then have individual entress and dessert. At your meeting, you could also ask about your dessert and alcohol options. Most places will not allow outside food (liability issues), but maybe they will allow a cake or create one special for you. All of this is doable, and the hospitality pros will walk you through it. Best wishes.