Yeah, magnetic saturation basically means the core material loses is ability to "amplify" the magnetic field, relative permeability, which would be originally several thousands. It does not happen suddenly but gradually, and even when all is lost, you still have permeability of 1.0 (that of air), so there is no limit to the torque, but you get less and less for given amps * turns. This means now you need to put thousands of amperes more to get what you would normally get by just adding 1A. Quite obviously, the resistivity of the winding copper wire is the problem here, and the windings just vaporize in seconds.
This "diminishing returns" game might already start at the rated current, or slightly above it. In absence of thorough specifications, the only way to know is to test and measure.
If you have a better-than-normal cooling available and efficiency is of no concern to you, then you surely can drive the motor into the "diminishing returns" region; the saturation is not abrupt but gradual. On the other hand, if you just mount some water cooling blocks outside of the motor, you may be overestimating your cooling efforts. The windings inside do not couple to the motor iron that well; there is a lot of air there, and some varying amount of varnish which might be better than air, but still crappy as thermal conductor. As most of the heat is produced in the copper windings, and their resistivity goes up with increasing temperature, forming destructive positive feedback, by exceeding rated current, hotspots form somewhere in the middle of the windings, until the varnish burns, causing short circuits, or the copper simply melts.