Out of curiosity, what do the rest of you do for tie-basing? Is there an impstar around whenever you run more than 3 4-tie Minion groups (12 fighters), or does everything need to be launched from an imperial garrison? What kind of imperial "pocket carriers" are available in Legends and Canon?
In the EU, a whole lot of capital ships, whilst not designated carriers, had at least some smaller craft with them for a variety of duties - not dissimilar from WW2 cruisers and battleships, some of whom had their own airplanes! This complement may range from anything such as the 4 carried by the Gozanti Refit or a Carrack-class Light Cruiser, to a squadron of 12 on a Marauder-class Corvette or a Dreadnaught-class Heavy Cruiser, to 24 on a Nebulon-class Frigate or a Victory-class Star Destroyer.
And then there is the modular Strike-class Cruiser, which in its standard configuration carries 18 fighters - but depending on how it is configured its starfighter complement may range from 0 to 36!
All these ships are or were used by the Galactic Empire, so this should provide you with ample options to choose from depending on how many fighters you want to throw at your players.
The new Rebels show has invented this:-
to carry 4 TIEs and provide a more manageable opponent for the shows protagonists than a SD.
That's not a new ship - but as much as I like to see the Gozanti featured, the new "windows" they added to the sides look really ridiculous when compared in size to the TIE cockpit or even the bridge windows. Is that a deck or a crawlspace?!
Easily adapted to Star Wars by replacing the mi-go with hostile alien space monsters from another dimension, or some such.
Or that Space Worm!