So, my internal playtest game had two very different characters in it. One was a wizard who was trying very hard to stay out of Council politics, even though he was a.) the only wizard in town and b.) the latest in a long line of famous White Council wizards. The other was an Emissary of Power, the Spirit of Las Vegas (the power source was a constructed(!) magical being who believed itself to be the soul of the city - but that's a story for another time), who was primarily tasked with helping to maintain balance in the power structure of the city.
So, what bound these two characters together? Nothing. Nothing at all.
Except that they knew they could watch each other's backs and were a good contact to have. So what ended up playing out was that whenever the wizard got into shit, the Spirit would notice and be like, "Man, I better make sure that whatever's going on with this guy isn't going to wreck my town." And whenever the Spirit had things to deal with, he would call the wizard and be like, "Hey, back me up while I'm dealing with this shit."
Never underestimate the gravity of reliable professional contacts.
Note, that isn't to say that having an overarching tie is a bad thing. It just may not always be as necessary as you think.