We generalize the six degree-of-freedom God-object approach to enable its use for multi-finger interactions in virtual environments. The connected finger phalanxes are modeled as multiple constrained God objects. The mutual interdependencies between multiple God objects are resolved using Gauss' principle of least constraint. This generalization of the God-object method allows us to avoid the penetration of multiple fingers and their phalanxes with objects within a physically simulated virtual world. Our observations indicate that the generalized God-object approach leads to plausible collision-free positions and motions of the phalanxes of the user's fingers during complex six degree-of-freedom manipulations, while artifacts such as artificial friction or a stuck hand are avoided.