In countries where meta-strikes are legal, the unions cooperate on basic right, and strike together when needed. Such coordination is explicitly illegal in the US, and has been since the '30s (IIRC).

It sounds like they'd at least have more power than a single-employer union, by virtue of being larger and having more resources.

I'd much rather run a factory where only 10% of my workers may strike than one where 90% may strike.

It is usually like 2 or 3 and they will strike together. Having multiple keeps the unions in check and arguing for a pay raise for 60% of workers and nothing for 40%. I that case, the 40 would form their own union