Not really sure how I did it but in my first 4 player FFA I got 2 of the players to give me a cease fire. You definitely need to max out the Diplomatic research (as do they), then try and get a trade alliance as soon as possible. As I wasn't attacking either of them nor were they attacking me, eventually the military assistance bonus was high enough to get a cease fire, after which the AI eventually sends envoys at which point your relationship problem is no longer an issue.

He probably liked you just fine, its just that you didn't like him very much. The player is now under the same relationship status system as the AI is, and things like envoys, missions and bribes only effect how they view you. The trick is to get the AI to do those things as well.

But yes, modifiers like adjacent territory and military actions means its much easier to get alliances with players that are farther away. The reason you could get a cease fire with that advent player was simply you actually liked them more than the TEC player you were buttering up to, even though that TEC player liked you more.

For example you and the Advent probably both had a +5.5 or something relationship modifier, good enough for a cease fire, while the TEC AI probably had a much higher, say +10 towards you while you only had a +2 towards it. Since both players need to have the required relationship level, you wouldn't be able to get the cease fire no matter how much you tried to befriend him. Your TEC "friend" basically needed to return the favor before that happens.

Well think of it this way. Before you were like a totalitarian ruler, able to solely decide who you wanted your friends to be because you were the only one that mattered. Under the new system, you still control all the action, but now how your people feel about a given faction influences your diplomacy. As an extreme example, before if you spammed enough envoys you could raise an enemy's disposition high enough to stop a war on a dime just because you thought it was politically convenient. All that mattered was how your enemy felt about you. Now, in that same situation, the people of your Empire might not want to stop fighting an enemy that's killed their friends and family unless they do something to redeem themselves.

In other words, now both you and your enemy need to spam envoys and other methods of mutually improving relations, not just unilateral action by yourself. I'll admit I'm still figuring out the system as well, but early on get all the relation modifiers upgrades, then try to befriend an ally that you won't be having skirmishes with. This can be frustrating because if an AI you want to ally with decides they want to attack you your basically out of luck and need to find a different friend. Eventually, just because of the damage you inflict on other factions will improve to the point of getting trade relations and cease fires, at which point you can easily start full alliances with whomever you wish.

But be careful, every treaty you make with faction A will hurt relations with their enemy faction B. Trade alliances and cease fires are combined are only -0.25 (though its per player), but any more than that will start getting serious penalties. Hopefully this means you will no longer be able to ally with every AI player now, and it should lead to groups of allies instead of the haphazard diplomacy of before.

That's what I think. A couple of details will be smoothed out in the next hotfix, but even as of now I think its a better system.

While that's certainly arguable, as of the last patch, human players had a huge built in advantage in Diplomacy over AI in that they could freely do haphazard diplomacy while the AI was completely frozen by this relations system. The result was that it was incredibly easy for a human player to ally with every single one of the computer players while they were still all at war with each other. This is obviously in your "best interest", as you can ensure you are apart of the winning team no matter what happened, but is horribly unrealistic and bad for interesting gameplay.

Part of this was the bad design of the relations system not taking into account your other alliances, but the main thing I think was the complete freedom human players had in comparison to the AI.  While the ideal solution would be to make the AI as capable of understanding Diplomacy as the player, sadly that's just not possible with today's technology, so they had to restrict the players' freedom somewhat. Also attempts to give AI a compensating advantage with each others Diplomacy via handicaps tended to lead to AIs ganging up on the player, which is probably the worst possible outcome.