Any recommendations for a restaurant in the New York City Theater District that welcomes large parties (30-40 persons)?

For that many people you're probably going to have to take a private room.

What kind of cuisine are you looking for, a set dinner or ordering off a menu, and what is your budget?

Also, for this many people you'll have to give a credit card up front and decide who is going to control wine/drinks (they won;t do 20 separate checks - so someone will have to be the responsible party - and you will have to have some sort of alcohol rule up front or a couple of big drinkers could send the budget through the roof).

It would help to know budget, type of food/ambiance etc.

Carmine's would be my first thought for southern Italian served family style. For something a bit nicer, Trattoria Dell 'Arte is just a bit north of the theater district and has several private rooms and very good food. The same owners have several other restaurants including Bond 45 that's closer to the theaters, also Italian.

Keen's is a great, historic steakhouse just south of the theater district. They have some great private dining rooms that would work.
http://www.keens.com/banquet.html#

Ruby Foos can accomodate large groups

I've been to Bond 45 with a group of 12 and there were other, larger groups there. A few years ago I went with a group of 30 or so to Victor's (50th St, Cuban food) and we were seated in the main dining room, but it was after a matinee so our reservations were for 5PM, which may or may not make a difference.