There is no NG+, but there is a secret character in the game that can reset up to 3 paths, so you can try out some of the mutually exclusive paths. If you make use of this character, make sure to talk to him as well, since he'll give you a bad end if you just use his powers 3 times without making friends. If you need directions, search the "Temple of Spellbinding" in the walkthrough.
Viewing post in Caliross, The Shapeshifter's Legacy comments
It doesn't cover all paths yet. Currently you can reset the Cowgirl path, Eliza's path (the futanari), and the "ghost possession" path (you can also reset your "slut reputation", an invisible stat, if it goes too high). I should add the vampire path to the reset list pretty soon, as well as the werewolf path (this one will have to wait until the path is finished). With those in, I think we'd cover all the paths that can narrow down players' options.