It would be interesting if nations would have a few (like 1-3 per nation) military bases of their own, and based on happiness, you could use some of their services. Like...your craft could refuel at their bases, giving them higher effective range (as long as you don't use antimatter engines and happiness is kept over certain level). They would also slowly upgrade their bases to match aliens a bit, like using better radars (probably even less range than offbase radar instalation), SAMs (and very later, if researched, laser batteries), and even an interceptor or two. Based on their happiness, they would relay radar data to you, or even take more active role. Like, nation with 100% happiness would detect an ufo, give you its position and attempt to shoot it down. When ufo is downed on their territory, they will even send their own military to support you in combat. If nation is NOT happy tho, they will not tell you about UFO, try to shoot it down and recover for themselves, thus effectively creating an opposition to you.
I dunno if something similar was proposed already, I tried some searching and found nothing.