You can't keep any legendaries. Some are available to be caught, but they won't stay with you for long.

Zekrom is available for two fights in the story and that's all, it leaves your party after that.

Each region has a single legendary (Rayquaza/Mewtwo/Keldeo/Arceus) that can be caught roaming in the wild — if you do, you can't refuse duels, and if you lose, it goes to the winner. Also runs away if bored (you stay unchallenged for too long or log off).
https://forums.pokemmo.eu/index.php?/topic/81062-legendary-pokemon-guide/

If you want a "seen" entry, check this:
https://forums.pokemmo.eu/index.php?/topic/75473-list-of-hidden-pokemons-for-pokedex/

In the future devs want to add dungeons, Mystery Dungeon style, where you'll be able to catch some non-Uber legendaries — if you manage to defeat them.
More info on that: https://imgur.com/a/NBIRZAq