Electromagnetic torque is produced at the interface between field and armature fluxes or, considering that at least the armature is an electromagnet, as the product of electrical and magnetic loading. Torque estimates from geometry can be made, proportional to D2L, as an estimation of the airgap shear stress. With either buried conductors in the rotor (induction machine) or interior permanent magnet machines, the increased permeability of the rotor iron directs the field flux out through rotor poles into the airgap. It is the (attractive) interaction of this rotor field flux with the rotating armature flux that produces torque. Since the magnetic circuit of the field flux is held and guided by the rotor iron, I see how you could say that the armature flux acts on the rotor iron instead of directly on the conductors. I would technically agree with that (in the same way that the reaction on the stator side is primarily through the teeth, since they effectively carry the flux) but I don't know if it really gets at the heart of the matter. There is also reluctance torque to consider, which I'm not directly addressing here.
So then, with this thinking, it's easy to see that increasing either the field or armature flux in the airgap would lead to an increase in torque. For permanent magnet machines there are a few obvious ways to do this (more magnet material, stronger magnets, etc). The armature flux is dependent on current and the number of turns. Increasing either will earn you more torque. Any material changes that lead to increased flux in the airgap will lead to more torque such as, for instance, steels with higher permeability.
There is of course no free lunch. Higher flux densities, besides when they approach demagnetization limits and thermal issues, will lead to higher BEMFs - so that it will take more voltage (and therefore more power) to operate.