You have an Ithaca Model 37 featherweight 16ga and the buttstock is broken near the receiver Will a 12 ga or 20 ga buttstock fit the 16 ga receiver Is another company reproducing Ithaca style firearms?

Yes. Yes.

Ithica used the same basic receiver for their 37s. You can find a used butt stock and with minor fitting make it work. Many manufactures produce after market stocks both wood and synthetic. Try looking on eBay, there is a seller making aftermarket stocks for Winchester mannlicher rifles. i don't remember his screen name but he will do other models as well. He uses a copy-cat machine but his work is good, however the stocks are not a "rare find". They are current production.

Numrich (gunpartscorp) shows different part numbers for the 20, 16, and 12 gauge stocks. They claim to sell all three although they are sometimes out of stock.

http://www.e-gunparts.com/productschem.asp?chrMasterModel=076Zz37