Per Operational Turning Points: Hanseatic Crusade, most of the Galaxies in the Goliath Scorpion touman of the Dark Age and IlClan Eras use a bespoke Cluster/Trinary organization: only Seeker Galaxy uses the "standard" Clan Cluster/Trinary setup.
Of those, Command Trinries include two BattleMech Stars and a single Composite Star: 2 'Mechs, 2 Points of Elementals, and 1 Aerospace Point.
That said, at the Trinary level, mixed forces are the norm: the exact balance of BattleMech, Elemental, and Aerospace Stars varies depending on the type of Trinary involved.
As for Seeker Galaxy, many of their MechWarriors opt to pilot vintage Star League BattleMechs rather than Clan OmniMechs, even when given the choice, due to their adherence to the Seeker mindset. (Or perhaps since it's easier to make off with the latest batch of isorla when your 'Mech has hands and arms with which to carry it...)