It seems that team count is locked at 3, no matter the format. Kinda unfortunate.
Side note, something I didn't know; Secret Pals from other bases (as in not your own) have pre-set teams pulling from Seedot, Shroomish, Slugma, Wailmer, Azurill, Igglybuff, and probably a few more. This means any Blissey Bases you scan/otherwise get into your game, only the leader will actually have Blisseys. Unfortunate.
Let me know if I'm misinterpreting what you're saying:
Suppose we attempt to create sort of a "Gym" base, and we gathered Secret Pals with teams corresponding to the team theme, their teams will, in reality, have a random pick of three from the list you've provided. In truth, you--the owner--will have the only Gym-type team in the Base; so that means the player will inevitably be battling under-evolved Pokémon if the player, the owner, or both, uses strong--maybe competitive--teams in the base (not like you're required to battle them, anyway).
If so, this is definitely unfortunate; I had planned to create a Sandstorm Gym with five members--Gym Trainers--having a team of their own. I knew the team limit was three, so I planned to put in Landorus-Therian, Excadrill (Mold Breaker), and Mega Tyranitar, all in that order. (If I had an official at the beginning, he'd say that my team is all weak to Water and Heavy Rain.)
EDIT: Also, I find it convenient to be searching up and down for Blissey bases. If we gathered as many as we could within a day, we could all start boxing tomorrow. I'll see what I can find in the meantime. I'm not playing the game at the moment, as I'm trying to keep a promise to the Spriting Team to finish my QC of MegaTar over the break.
NOTE: Also, there's an easy leveling trick to help raise your Blisseys to Lv. 100 should the need to contribute to the Blissey Base Project interests you. This works in the same manner as the Centrico Plaza in Pokémon XY, yet is--arguably--a better method in ORAS. Deposit your Blisseys in both of the Day Care Centers provided in-game, and set your system on an infinite loop around the Battle Resort. To do this, start in a corner near the Day Care on the right, and hold either right, left or up on the Circle Pad or the D-Pad. If done correctly, the player should continue biking around the island with no interruptions.
Source
Blissey Base Collection