To get more gear ability slots for your favourite pieces of clothing you have to get your hands on a Super Sea Snail. These are awarded at the end of each Splatfest to participants based on their Splatfest title and on whether or not their team won. You can also get them by reaching Rank 30 in multiplayer.
Once you are Rank 30 go to Judd the Cat in Inkopolis Square who will reward you with a single Super Sea Snail which you then take to Murch who you can find in the same location. Murch will then let you unlock a new ability slot for one of your pieces of clothing. If you now return to Judd every time you level up he will reward you with another Super Sea Snail.