I just played a game where I played the Terran Alliance. I was right at the center of the Universe and I managed to keep all the major civilizations in a friendly disposition towards me.
I researched the techs that increased my diplomacy and 2 levels of miniaturization that allowed me to convert scouts obtained from other races into trade modules that had no engines. I quickly had trade routes with most of the civilizations.
I build up my army by trading ships from other races. Whenever a race would start to catch up militarily, I'd buy ships from them. Having the most powerful army discouraged extortion attempts.
Right up to the end, when I was 10 days away from an influence victory, I allied with all of the major races except with the Korx who were warm towards me.
Then something strange happened:
The Carinoids went and attacked the Krynn who were one of my allies. This is strange because the AI didn't appear to take into account that the Krynn had a powerful ally even though they themselves were weak.
So I took out the Carinoids, and went on to have my influence victory. Asides from that one skirmish. I didn't engage into battle any of the major races in the game.
The difficulty level was "crippling" with my 9 opponents set at "Genius" level of intelligence.