Most airlines that belong to a global alliance – Star, oneworld, SkyTeam – partner mostly with airlines inside of that alliance. They may have non-alliance partners as well, though those are often limited. For instance American Airlines partners with airlines such as Air Tahiti Nui and Etihad which aren’t part of any alliance.
There’s only a limited number of cases where an airline that is a part of one alliance partners with an airline that’s in another alliance.