The alliance system in MTW is bad about "ganging up" on a few factions, including your own of course. The best way to "work it" is to make sure you have more allies than the enemy you first attack. That usually causes the AI to break alliances with them rather than you.

After the first few decades, you end up having to wait for the AI to ask you for an alliance. Your chances of getting one other wise are close to nil, no matter how much influence you have, or how much logic there would be for the AI to accept it.

On the plus side, this does make the AI a bit tougher to beat. Usually the game goes like this for me:
1. I target a faction early for elimination and assimilation. I time it so that I have more allies when it happens.
2. Subdue first faction retain some allies.
3. Target another faction, lose all allies.
4. At the point the other faction is collapsing, one or two AI factions attack every border I share with them--no matter how crazy the attack.
5. As I cripple the attackers one at a time, I'm attacked by new enemies at just the point the old enemy is collapsing.

This continues until I win. The really unfortunate thing is that it is predictable. It does make the game a bit tougher, but I wish if the AI was going to attack, it would do so before the other faction reached the point of collapse. It is the lack of logical motive on the AI faction's part that is disappointing.