The conflict between the Brazil/Caliphate alliance and the Centauri Federation could cause things to heat up fast. Seems like a smart move by Brazil; three planets makes them a ripe target, and there does seem to be a decent chance that the other powers wouldn't interfere, especially if they're all busy with their own expansion.
Just looking at the updates, it's possible it could expand to include Mars on the Centauri side, and possibly Japan on the side of the Terran faction (The Federation has been working on diplomacy with Mars, but has contested colonies with Japan). Unfortunately Mars has (quite reasonably) focused on immobile defense bases, and couldn't do much in the Centauri system, though their patrol ships would be a huge pain for enemy supply lines in Sol.
Taking this into wild speculation territory, because I'm bored, I'm looking at what those powers can bring to a fight.
The Federation navy is exclusively missile armed, which I suspect would serve them well in a defensive war. Aggressors would be away from their own sources of supply, but the Federation ships could replenish their missiles from their own colonies, and would be well positioned to win any war of attrition. They also have massively better sensors than their potential opponents. I find it surprising they haven't constructed any defense platforms considering how big a target they are, but I suppose with multiple habitable worlds their planners may think stationary defenses are an invitation to defeat in detail. As of the last update, their armed vessel tonnage is at 91,800, though I wouldn't be surprised if they have added another cruiser for a total of 102,000. That's slightly deceptive, though, since their jump ships are unarmed but useful due to their powerful sensors.
Brazil's railgun and gauss armed vessels provide potent point-defense coverage against Federation missiles, and they have a slight speed advantage so they could potentially chase them down if the Federation tries to engage them in deep space, or if they manage an ambush. Their navy currently has a combined tonnage of 102,000, with 36,000 tons currently under construction. A respectable force if they can manage a decisive battle against the Federation, and their powerful PD capabilities mean it's entirely possible they could stop all but a trickle of Federation missiles.
The Caliphate's FAC based navy is tricky. It currently has 90 armed FACs, but can't transport them all at once, and its ability to maintain and resupply the ships on site means they could be a thorn in the Federation's side if used well. Their missile armed FACs could almost certainly pound the Federation ships without coming under fire themselves, and if the Federation leaves orbit to try to chase the carriers down (assuming they can even find them, even with their sensor advantage), they'll lose most of their defensive advantages. Their combined tonnage is probably around 87,000 tons, but being FACs can likely hit above their weight class. They have about 11,000 tons more under construction, but the real limit is carrying capacity; their carriers can field 84 FACs (96 once their additional carriers finish), of which several will be unarmed sensor craft.
In the land of ideal battle planning, Brazil and the Caliphate combined could probably easily deal with the Federation using smart tactics; the Caliphate's missile FACs let them pound the Federation at range, while Brazil's navy can run down and destroy the Federation's if it gets a chance. On the other hand, Steve might easily have them split up, since it's probably not realistic that they would cooperate closely, and each hit a different planet. In that case, I think the Federation might have a chance by wearing down the enemy ships while avoiding a decisive engagement. The Caliphate carriers are also extremely vulnerable target, and the Federation's sensors and likely DSTSs on their colonies means they'd have a definite recon advantage. It would still be extremely difficult for the Federation navy to get past Brazil's potent point defense, though.