Is there a limit to the amount of charge that could be stored in any system as a result of the charge particles repelling each other?
There might be physical limits hit when you have a very high charge density in a small space, but there are much more practical problems: how do you get the charge to stay there?

In the simple model of a capacitor, there are two plates on which a charge is stored. Between the two is some insulating material, usually a dielectric to increase performance of the capacitor, but it's possible to have air or vacuum capacitors too. The limit on how much charge can be stored is determined by the breakdown voltage between the plates, which depends on how good the insulator is.