Hello I have the same size of tank and I keep 4 corydoras that are bottom fish and 6 female bettas, I have no problem with any fish there. I have lots of plants there so that bettas can hide if they are being chasen by other bettas. Corys and bettas are doing fine together, no bullying, they seem to like each other.
Well you probably don't want to get many more because even though it doesn't look crowded in that size of a tank, the fish will be. Ive heard that each fish should get at least 5gal. So that its not overcrowded. I have a female Betta too, and when I added a male fish (swordtail) the Betta instantly went after it, and I fixed that problem. You see bettas are territorial and when they have been in a tank (there territory) longer then another fish, and you place a new fish in, they respond by thinking that the new fish is intruding and will attack. So what you should do is take all 3 bettas out, add some new fish (maybe 2 or 3 depending on size(and of course avoid male bettas)) to the tank and maybe switch around some of the tank decorations so that the bettas may think there in a new area. Then close around the same time put the bettas back into the tank, and see what happens. My tank (10gal) has one girl (Betta) and the rest are all males, so I would think that it did not matter the sex of the new fish. I have also heard that angel fish are an ideal thing to have with bettas - because the angel are known to get curious and they may peck at or nibble on the bettas unique fins (since usually they are long and attractive)
If you are getting 3 females you might consider getting 3 males as well. Otherwise you might end up seeing some bloody carcasses. FYI Bettas can get pretty aggressive without a mate. Hope this helped!
