So, this suggestion was actually heavily inspired/ripped off from the Cabal interactions from Ship and Weapons pack as well as the fact you can pay a Tithe to Luddic Path fleets to be left alone.
Basically have it so that when a Pirate fleet intercepts the player fleet they try too open comm's with the player. If the player accepts they then demand one of a number of things: Either all of the players cargo, a large percentage of their credits, Blueprints, Supplies or one of the players better ships. The player could either accept and the pirate fleet would leave them alone for a little while (and if they took one of the players ships that would be added to the pirate fleet) or if the player declines it goes to combat as usual.
The way I see it it solves two things. Makes the Pirates feel more like pirates and less like generic enemies. And second of all it allows an early game player to escape from a Large Pirate fleet without having to fight a retreat battle where they might lose their entire fleet, though of course the Player still has too give up something precious to them be it credits, a nice ship or cargo.
Even better if the Pirates could extort non-military npc fleets such as traders and scavengers as well.