It'd be pretty hard to squeeze in additional mediums in the game right now. Battania's Medium Infantry is also the team's skirmisher, while Khuzait's infantry balancing is in a very delicate position.
Empire: I guess the best option would be to have the Menavlion Infantry be let go, though it might make the Legionary feel redundant. Menavlions seem to be a huge part of the Empire's identity and removing that would just leave you with a more infantry-focused Vlandia.
Aserai: Unsure where a medium infantry can fit with them, since skirmishers/shocks/peasants are typically light infantry troops. I guess the closest thing to giving Aserai a medium infantry would be to buff the Heavy Mace perk, since it kinda feels a bit worse than the light archer's default mace.
Sturgia: Brigand can easily be replaced IMO. Berserker already has the downside of "Ragequit if you die as this unit" and Hunter with the shield perk is already a better melee fighter than the Brigand. Throwing axes could also be moved to a theoretical Sturgian medium infantry as a spear replacement, though the problem there is that my suggestion might actually make Sturgia good, and we can't have that.
Vlandia: Considering that they're already the best faction in the game right now, I don't think they even need a medium infantry.