A lot of older Broadway shows from the 20s - 50s had large casts because they didn't have to pay them as much.  I would suggest Once in a Lifetime by Kaufman and Hart.  LOTS of roles for men and women.

There are 18 possible scripts listed here.
It's a mixed bag, including sketch shows and other relatively trivial items.
Personally, I would look at "Beasts" from that list - a collection of plays based on short stories by Saki, with some excellent acting opportunities.

I directed The Skin of Our Teeth by Thornton Wilder last year, and it has a minimum cast of about 14 as written, with room for plenty more. I think we went with 18 or so with lots of doubling, PLUS our AD and I (as the director) played "ourselves."  (Some of the actors go out of character at times).

I will note that it's a fairly complex piece -- it works best with a video or film segment to intro, and at least some graphical background to start act 2, plus as written, the set is falling over and reconstructed at various points.  But it's VERY layered and interesting, and I truly enjoyed it.

If a Christmas show interests you we just did Miracle on 34th Street by Snyder, Sevrin, and Vreeke. The script says there are almost 50 speaking roles plus there are a number of non-speaking roles. I had most actors play multiple roles. Audiences really enjoyed it. It's based on the book so there are some differences between it and the movie but not so much that it bothered the audience.

We just did Get Smart, and it was great fun! We threw in a lot of extra phones: chopsticks, ties, guns, everything. But Smart is in every single scene, and you need a really strong actor who is very committed.