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Provided you take the rules into account and you have the force organization.

Is there a limit on the number of different allies you can take?

There are no universal Ally rules, so you'll have to follow the ally rules for each particular army that allows you to do so.

Be aware that the Daemonhunter online FAQ forbids them from allying with any army that already has other allies.

That's interesting as the DH's RAW are the only place we could find a reference to actually taking more than one set of ally.