If you enforce client-side biometrics and can somehow make sure that an actual fingerprint reader has to be used on the client side, and that I (as an evil user) cannot alter the behaviour of that fingerprint reader at will (despite the reader being physically in my evil clutches the whole time), then I'll just have my cat put his paw on the reader at the right time, granting me an extra vote.
So no, you cannot prevent multiple accounts with client-side biometrics.
You can block some attempts at multiple accounts through various mechanisms, which can all be worked around (and may backfire at times), but only with efforts. E.g. you can prevent multiple account registrations from the same IP address. Or you can ask for a token payment of 0.01$ from a credit card, and allow only one registration per credit card (but then, there goes anonymity).
At one point you have to ask yourself the extent of the anonymity that you want to preserve for the users. If users are completely "anonymous" then, mathematically speaking, the notion of "multiple accounts for the same user" becomes ill-defined. Anonymous users cannot be distinguished from each other, and that's kind of the whole point.