Of course, playing with diplomacy is your friend imo...
i mean I'm currently playing a game as TEC with 6 hard AI unlocked teams
and all i keep doing is completing missions for all of em, result is having em all in my pocket, then when i see one of em is becoming too strong, war time... unleash all my cannons unto his planets a solar system away but still... and order all my allies to target him by selecting his ships and giving him rally points, and THEN i come with my fleet, which doesn't hold much power
as a result, i have only allies and i slowly kill em one by one by declaring war on one of em..
as one falls i colonize everything giving me more economy more artifacts ( still want to achieve the goal to have all artifacts at once

) and of course, more Cannons to auto cast lol ( currently got a total of 22 cannons on autocast, yeh ok, it can take nearly half an hour before all missiles stop reaching a given planet so i can colonize it but... shit, good way to slowly exterminate em all!)
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Oh and regarding your question just above, depending on the AI and what he requires, he will give you different missions such as
-Give me X Crystal
-Give me X Metal
-Give me X Credits
-Destroy X ship of the player Y
-Destroy X defensive structure of the player Y
-Destroy X logistic structure of the player Y
Those are the ones i saw... you mostly see em ask for ressources for early reputation gain from my past experiences... and after like 60% or so, all they ask you to do is destroy opponent factions so... but thats from what i noticed.
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And in order to keep an ally... simple, do the missions he requires you to do... oh and by the way, when they ask you for ships to destroy, i noticed that you can kill anything from that player's color and it will count as a vessel... doesn't work for the other 2 missions though, unfortunatly