Don't you imagine every species does that?
Turian Exceptionalism: Take their canonical militarism and crank it up to eleven, then mix with the British empire, Starship Troopers and Destiny's Cabal. They've launched an openly expansionist unification war against the entire galaxy. Defeated aliens are culturally imperialized, they've got volus, batarians and quarians in the empire and effectively, they act and are treated like turians, complete with facepaint, recruitment into the military and loyalty to the Primarch.
Asari Exceptionalism: The Thessia Beacon is common knowledge and for the entire history of their civilization, they've been using every scrap of prothean technology it taught them in total war preparations for the reapers.
Salarian Exceptionalism: Sparks.
Krogan Exceptionalism: No genophage. They win their Rebellion, then they and the survivors of every other species start opening every Relay they get their hands on in the hopes of finding more living space/avoiding the apocalyptic horde of krogan everywhere. Then one turian specter finds a bizarre alien weapon, an autonomous, biomechanical dreadnought which claims to be one of an entire species of same, theoretically capable of winning the war...
Quarian Exceptionalism: They retain control over their AIs. They're still fleetbased, but here it's by choice and they're basically an off-brand version of the Culture. Sure the Council disproves, but they do so quietly because of the von neumann killbot army. Also, they've still got suits, but here they're more along the lines of Forerunner armor.