Well. I believe that we got a clear hint that our assigned forces are not enough for this task.
Who shall we ask for assistance?
Salamanders hate dark eldars, but we already asked them for favor, so....
We don't necessarily need a favor to ask for military aid, but in the Blazing Wardens' case, they are from another Sector, so it would sadly probably require one. On the other hand, Aetelian locals don't have that kind of problem, since this is where they are based anyway. Basically we send requests and depending on our relations and our Fellowship, they will be answered even if we have no favors held. And thankfully we have mostly good relations all around the Sector. So with that in mind...
[X] Plan Death To The Alien
-[X] Call for the Order of the Thorned Spear to join the Mist Shrikes in crushing the Genestealer uprising on Lezo
-[X] Request Lord Admiral Adherbal send a battlegroup to Zatloczony Tertius to bring the attacking Eldar ships to heel
-[X] Tell Lord General Tavisolta to send reinforcements to Lezo, and only if there are still men to spare after the mustering for the Sector Capital, send some to Faisal and Seibourc
I didn't include the pirate mission because there's already Adherbal's nephew assigned to it in the description, and most of our other good relations are not the sort of people that can send out an army or a fleet to wherever they want. Also we have a Major Favor with the Sisters, so even if they for whatever reason didn't want to incinerate some Xenos and mutants, we could call it in.
Looking at you, Harker and Kalivnova