For a really odd ball, but plausible ~ if in only the sense of politics making strange bedfellows ~ the Terran Hegemony under a string of democratically elected Rulers could actually forge an alliance with Taurian's.
Specifically a military alliance. Heavily Naval in form as well.
The prime driver for this would the FedSuns, and as a side matter the Cappies. From the TH perspective the TC is in a number of ways an ideal ally against the FedSuns.
The TC is nowhere near the TH, yet both states border the FS.
Apart from having the second highest GDP per person, the TC is also a literate, technically skilled state. Selective aid via second hand Military Technology, can be implemented out of the TC's own budget without threatening TH technological dominance.
Not to mention the TC is perhaps the only Naval force to match the TH in skill.
Forcing the FS to deal with two distinct Naval threats at the complete opposite ends of its borders at the same time, is an ideal state of affairs for both the TH, & TC Naval operations.
One that leads the FS Navy to either disperse to deal with the two separate threats and face defeat in detail, or bottle up the fleet having them protect core systems of FS and unable to give either the TH or TC Navy`s battle.
This of course relies on the both the TC and TH swallowing their prides for Military Advantages.
On that note here`s an AU thought I had @ work.
Ian Cameron early on his process of forming the Star League, perhaps even before he becomes Director General, meets the Protector of the TC and oddly enough strikes up a friendship.
In attempt to draw the TC into his vision of humanity united, Ian is actually forced to address the core concerns aka economic / political / military needs of the TC, & perhaps even more importantly address and expand the difficulties in pushing forward Colonization of new systems.
Like oh say FTL communications, and sharing advancements in Terraforming and other critical bits of infrastructure. Or extensive military aid in further the TC's Navy.
Not to mention the free and open trade with other states, which is a very good thing for TC Industrial concerns at this point in time.
Whatever the incentive, from the 3rd Andurien War onward, Ian Cameron aided by Michael Calderon's suddenly even more deadly navy (Hello Battleships!), box the FedSun's into either accepting entry into the Star League from a somewhat weak position or accepting entry into the Star League after it's Navy gets it's ass-whooped by the TC.
A few friendly visits by Taurian Battleship squadrons leads the OWA Alliance and MoC to a very reluctant entry into the Star League. Without the TC a war of resistance is even more futile.
So we get a Star League overrun by bandits, mercs, and masses of unemployment in InnerSphere states. The Star League Army isn't a vastly admired and respected fighting force forged out of bloody war, but constant bandit raiding. Severe economic disruptions occur as Tariffs get removed, trade opens up and competition gets real nasty.
The only two states who really came out on top of the deal are the TH and TC, while several other states got the short end of the stick.