Check this thread: https://forums.sinsofasolarempire.com/400975

It's about capship supply points, but I think fleet supply is also mentioned, and works exactly the same way anyway. The relevant .entity files are RESEARCHSUBJECT_MAXSHIPSLOTS"RACE""Index 0-7"

For a general increase you could also change the following lines in the Gameplay.constants file:

    fleetSupplyData-Small
        fleetSupplyScalar 0.75
    fleetSupplyData-Normal
        fleetSupplyScalar 1.0
    fleetSupplyData-Large
        fleetSupplyScalar 1.25

These are the multipliers used when you select small/normal/large fleets in the game creation menu.

In addition you may want to look at varying the number of Capitals in game as well, the files are the

RESEARCHSUBJECT_MAXCAPITALSHIPSRACENAME 0-7

researchModifier
    modifierType "CapitalShipMaxSlots"
    baseValue 1.000000
    perLevelValue 3.000000                 (This value determines the number per level, just like the ships slots noted above)
researchModifier
    modifierType "CapitalShipMaxSlotLevel"
    baseValue 0.000000
    perLevelValue 1.000000

p.s as for a way to do it in one fell swoop? Sorry haven't found that yet,    I know it is a LOT of work, i have lost countless hours to tweaking and changing and re-changing those files. I have thought of asking IronClad for a job, but of course they have TONS more hours than i do.   

Haha, anyway, if you want what you want, time spent changing files is the only way i have found, be happy you can get what you want. 

-Teal

There is no easier way. You can however, as I already explained in the other thread, change the baseValue of the RESEARCHSUBJECT_MAXCAPITALSHIPS index 0 to allow a huge amount of caps from the start, which isn't feasible for fleet supply because people can actually build up to that number, while capships are still limited by fleet supply themselves.

That will of course make capship techs next to useless, but if you want an epic capship armada without much effort it's the way to go. You can also change the baseValue in RESEARCHSUBJECT_CAPITALSHIP_MAXBUYLEVEL"RACE"0 to allow buying all levels as you can't level 20+ caps to 10 with normal means unless you have an AI run into a Starbase for hours on end.