Small mods for things like this typically aren't published (because the game gets updated so often), but you only need to change a couple lines in a few files to be able to do what you want.
1. First download the reference files here. If you have Trinity use Diplomacy.
2. Go to your mod folder. You can find the path by going to the mods tab in the main menu and clicking the "Show Mod Path" button.
3. Create a new folder called "Bigger Fleet Mod" or whatever. In that folder, create a folder called "GameInfo"
4. Extract the reference files somewhere and copy these files... Gameplay.constants and every file between RESEARCHSUBJECT_MAXCAPITALSHIPSPHASE0 and RESEARCHSUBJECT_MAXSHIPSLOTSTECH7.
5. Paste these files into your mod's GameInfo folder.
6. For the capitalships, you'll need to edit a few lines that look like this. So open the file RESEARCHSUBJECT_MAXCAPITALSHIPSPHASE0 in notepad.
researchModifier
modifierType "CapitalShipMaxSlots"
baseValue 1.000000
perLevelValue 1.000000
Base level is the amount of capital ships slots you start with (in this case 1), and should only be adjusted on the researches whose names end with 0 (AKA the first ones, all the others should have values of 0). The per level value is how many additional capital ships you get by researching it. Thus if you wanted to double the capitalships you get just double the values in each of these lines. Note that each race has its own set of techs (PHASE is Vasari, Psi is Advent and TECH is TEC), so you'll need to make this small edit to 24 files total (the ones that have MAXCAPITALSHIPS in their names, sort of a pain but doable).
7. For the fleet supply, you can either edit another 24 files (the ones that have MAXSHIPSLOTS in them), again doubling the values in this small section.
researchModifier
modifierType "ShipMaxSlots"
baseValue 100.000000
perLevelValue 150.000000
Or you can just edit the Gameplay.constants file, with these few lines.
fleetSupplyData-Small
fleetSupplyScalar 0.75
fleetSupplyData-Normal
fleetSupplyScalar 1.0
fleetSupplyData-Large
fleetSupplyScalar 1.25
The numbers here are what your fleet supply values get multiplied by depending on your fleet supply settings you choose in the map options (small, normal, or large). Double these and you'll get double the fleet supply you'd get at those levels. Note this doesn't change the number of capitalships you get, if you play one a large fleet supply setting after doubling these number you'll have twice as many capitalship but 2.5 times as much fleet supply.
8. After that assuming you only adjusted the numbers, you should be able to enable your mod and have double the fleet supply and capital ships. Do note that this may make the AI harder as they will build bigger fleets, and it may cause excessive lag on large, long games depending on your stats. If that happens of course you can just try a smaller number of disable the mod.
