One way would be to make the Pirate base some sort of half-planet/half-starbase, as it actually is (visually at least ^^) a base built into an astroid. (And asteroids counts as planets in SoaSE so...)
So therefore (these could be upgraded as the threat levels increase as well) it would be nice to see that the base itself had some defensive or offensive capabilities, such as hangars, weaponry, etc. etc. As said, these capabilites could increase as the threat level grows.
Also, as mentioned earlier, developing pirates would be awesome to see, pirates that get better and better equipment (I prefer unique equipment instead of just exact copies of the other races' ships. Modified versions of these could be sweet though, but it should be real piratey.)
And another suggestion could be that when a player captures the pirate base, he/she could construct one pirate capital ship (leftover by the pirates, they didn't have time to launch it before their station was captured, or it wasn't fully constructed or whatever, you get the point ) and get some frigates/cruisers as well. This can also add room for some tech tree upgrades only appliable to captured pirate ships (this may also apply to other capturable entities, such as ship graveyards and whatnot - the ship graveyard concept is seen in some mods, for example), and so pirates with their bases and their conquering can become a strategic option worth pursuing for players who can use it right.
Just a few thoughts on the matter
Also; as suggested earlier in the thread - they could nearly become a player of their own (in terms of offensive and defensive capabilities, not system capturing and such) as players pay them a huge heap of money to get them to attack an enemy of the paying party. However, pirates are backstabbers, so who knows, it may backfire... This is an interesting concept as well, to be sure. Hope to see something new about the pirates in the future