I haven't tried this yet, but find these lines in CAPITALSHIP_TECHCARRIER.entity
CommandPoints
StartValue 3.250000
ValueIncreasePerLevel 0.550000
The StartValue is how many squads you start out with at level 1 - and it rounds down. The ValueIncreasePerLevel is the rate at which new squads are added as the ship levels up. So for this example: level 1= 3.25 = 3 squads ; level 2 = 3.8 = 3 squads ; level 3 = 4.35 = 4 squads ; etc.
Alternately, you could use an ability to add extra squads. If you look at BuffPsiCommand.entity from the AbilityPsiCommand.entity (the Adept Drone Anima ability that adds extra squads to the Halcyon Carrier), it has this entityModifier:
numEntityModifiers 1
entityModifier
buffEntityModifierType "BonusMaxSquads"
value
Level:0 1.000000
Level:1 2.000000
Level:2 3.000000
but you can add more units to each squad but this will effect hangars and capitals as well.
You do this via research, and it does not affect all squads in your empire. From RESEARCHSUBJECT_PLANETMODULEIMPROVEMENT_PSIHANGARDEFENSE.entity :
researchModifier
modifierType "HangarFightersPerSquadAdjustment"
baseValue 0.000000
perLevelValue 1.000000
You can also make a new squads of heavy bombers or interceptors.
You can have up to 4 different types of squads on each ship/unit
Hope this helps!