I'd like to try this with current multi armed Aegis build with dual great swords.
Multiweapon Fighting reduce the penalty for fighting with multiple weapons1.
Thrashing Dragon Style allows you to make an additional attack with another weapon as a free action when you make an attack with a standard action or an attack action, using you highest BAB (but incuring penalty for Two/Multi weapons fighting as usual).
Combining the two, you can use a standard action2 to attack at your BAB-4 with your primary hand, then use a free action to make another attack at your BAB-4 with any other weapon, which would be an off-hand.
1: Worth to be noted. Multiweapon Fighting reduce the penalty for fighting with multiple weapons. The rules are poorly written since 3.5e (see this chat room, KRyan explained the situation, worth reading). Basically, it should be based on TWF but miss a lot of things and links to existing rules.
2: Attack action is an ill defined term that hasn't been fixed in the FAQ. There is a lot of questions about this issue in the Paizo forums, but the general consensus is that an attack action is a standard action, since all attacks are listed under standard in the rule. Full attack is a full-round action and not an attack action (again, following the general consensus)
Not really, or at least not in any useful way. Thrashing Dragon Style applies to standard action attacks, which typically only let you make an attack with one weapon. The feat allows you to make an attack with a second weapon of your choice. If you have more than two weapons, you'd only be able to attack with two as a standard action normally - in any given action, the rest of your weapons would just be sitting there doing nothing. And if you're only ever using two weapons for the attack anyway, then Two Weapon Fighting and Multiweapon Fighting are exactly equivalent.
I'm a bit confused about why you need Multiweapon Fighting in the first place, though, since you're only planning to fight with two greatswords. While it does you no harm to take it instead of TWF (and strictly speaking you might not have a choice about it due to oddities in the feat's effect), it also doesn't give you anything particular beyond what TWF does. It's more designed for if you want to use your four hands to wield, say, four daggers (which thrashing dragon style wouldn't help you with).
It's worth pointing out that if you fight with two greatswords in the manner you described, you'll take a -4 penalty to your attack rolls instead of the usual -2. Even with Multiweapon Fighting. There's a Path of War feat - Prodigious Two Weapon Fighting - that allows you to TWF with an oversized weapon without this extra penalty, but as written it unfortunately only works with one handed weapons. Presumably this is because the writers simply didn't consider characters with more than two arms dual wielding two handed weapons, so your GM might be willing to house rule that if you ask.