Only one type of animal unless its a rare case like Vulnera (V.B) who is a lion mixed Mermaid: http://www.mangago.me/read-manga/sex_pistols/mh/v06/c040/8/
Karen is a cat.
The other dog is Tarou. He works for the Madarame family and agreed to help:
http://www.mangago.me/read-manga/sex_pistols/mh/v03/c012/2/
http://www.mangago.me/read-manga/sex_pistols/mh/v03/c014/7/
This is Hidekuni. He is Kunimasa half brother and a were-cat like him and their father David Woodville.
http://www.mangago.me/read-manga/sex_pistols/mh/v03/c012/4/
Hope that helps ^^
it's quite confusing so please enlighten me: can they transform into two types of animal? cuz i though karen wa a snake and then she became a cat? also the other madarame bro. who norio thought was kunimasa transformed into a dog too. @_@ its sooo confusing!