Just as the scout has its own "exclusive" module, the cloak, assaults should have their own modules that only they would have the fitting capabilities for. These modules would be put in the equipment slots and act similar to how vehicle active modules work. The assaults could have active damage mods and armor and shield hardeners that could allow an assault to stand toe-to-toe with a heavy for very brief moments with long cooldowns, making assaults important for tactical engagements and making pushes for objectives. These modules could have a high fitting requirement and the assault bonus could be changed to lower the fitting requirements for such modules. This may be hard to pull off server-side purely, but maybe vehicle modules could be recycled into these pieces of equipment.

Edit: Possible criteria for tiers:

STD: Shortest duration, long cooldown

ADV: Medium duration, average cooldown

PRO: Longest duration, shortest cooldown (still considerably long)

All tiers would have the same boost in attributes between tiers, with higher tiers having longer and more numerous windows of opportunity to go beast mode.

All I've seen are fitting bonuses. These modules are more role-defining, making the assault the top frontliner,