Ok, got it. The Order's group that wiill be equivalent to the Sorcerium users will be... Are you ready for it? The Halves!
Basically, the Halves will be half-human, half-mythical creature. There aren't any natural mythical creatures in this world so the Halves are created by way of a dangerous ritual that can result in death of the one becoming a half if even one thing goes wrong. As such, most mages won't be chosen/volunteer for the honor of becoming a Half. But if they do, then they will have a definite advantage over others on the field of battle. In general, a Half will be stronger and faster than most humans and mechanical objects on the battlefield and Sorcerium won't affect certain abilities that Halves can use. What type of Half one becomes determines the ability one can use. E.G. A Dragon-Half will be able to literally spit out nonmagical fire at will. A Demon-Half will be able to take control of an enemy's body by biting them then going into a meditative sleep. Each Half will also have one or more natural features that also increase the number of capabilities they have. Ex: Claws, fangs, wings, tail, etc.
I may add more to this later, but what do you guys think?