As announced on the latest developer's diary, the upcoming update 3.8 'Gemini' will introduce two new co-op modes: https://forum.paradoxplaza.com/forum/developer-diary/stellaris-dev-diary-293-introducing-coop.1577064/

Cooperative PvE: all human players control the same empire.

Competitive PvP​: any empire can be opened to other players to join on the multiplayer game lobby.