F.W.
I guess you got plenty advice on this all ready but I still wanted to put my two cents in. I'm a hair stylist and I just wanted to add, incase you thought otherwise, that using a thickening shampoo will do nothing for hair loss. All it does is plump up or ruff up the hair a little to make it appear thicker. I think the best advice is to treat the situation internally because it's an internal problem so all the vitamin suggestions are great. If you wanted something physical, Nioxin is good, the Arbon is probably good, the Biolage that was mentioned is a great conditioner but not for hair loss and I don't know about the stuff the other hair stylist recommended, never heard of it. The most important thing is not to stress!
Good luck and have fun with you're new babies! Wow, what a handful!