And have pirates stance be 'cease fire' to all factions but the one being attacked. Likewise, any faction without a 'cutlass icon' would be as on a cease fire with the pirates. To attack them you'd have to 'declare war' by clicking on a 'fight the pirates' icon at the pirate screen. So, if ou are not the target, leave them alone, unless you are helping an ally.
Explicitly attacking the pirates would also have 2 side effects: They would hold a grudge against you, so the next bounty round will have 20% more effectiveness against you, and the one after that 10%. Second, a pirate fleet always has a specific target. By helping that target shrug off the pirates, even if he didn't ask for it, would give a positive relationship bonus.
If each pirate fleet can be considered 'independent', so as to not fight all pirate fleets at once, the 'fight the pirates' button could be at the right side of each empire on the bounty screen (the cutlass icon itself perhaps), so you can pick your fights.
And your ships get the experience.