Charged black holes have a limit of their charge to mass ratio ($Q<M$ in geometrized units).
You can't overcharge a black hole. Hawking radiation drives the mass down but gets suppressed as the hole approaches extremality (maximum charge per mass). Injecting electrons also fails: as charge builds up it takes more and more energy to push the electrons in. All this extra injected energy adds enough mass to prevent over-charging. Over-spinning a rotating hole fails for a similar reason.
Charged black holes always attract. Extremal holes of like charge have just enough electrical repulsion to cancel Newtonian gravity. But general relativity features "enhanced gravity" that grows strong at short distances and is in a sense infinite at event horizons. So (I think) extremal holes would still attract and strongly so when they get close.
What happens when two almost extremal supermassive holes, say with $Q=0.99999M$, are placed far apart at rest and allowed to merge? The resulting hole will have $2Q$ of charge. But the mass will be less than twice! Quite a bit of mass is lost as gravitational waves when holes merge. So $Q/M$ would exceed 1.
My logic must be flawed. Am I wrong about the "extra attraction" effect in this case? Without which the holes would merge slowly with little gravitational wave emission? But it is strange that two black holes could drift so close, horizons almost touching, without rapidly coalescing. It would also allow any number of extremal charged holes to be placed in a static constellation.
