[utjtylqu] many charges

in the real world, you can have masses which only attract gravitationally, or masses with positive or negative electric charge which attract or repel according to the parity of their signs.

if inventing your own universe for N-body particle simulation, you can have as many different charge types as you want, and you can choose the sign (or more generally, strength) of the interaction between each pair of charge types to be anything you want, even zero.  every particle could be its own charge type.

can weirdness happen, for example violation of some conservation law?  that particular question can probably be answered by applying Noether's Theorem.

quantum chromodynamics (strong nuclear force) has three charge types, called colors.  forces are not inverse square.