If there isn't enough current and you add a battery, you can expect increase in torque because the voltage supplied by the batteries will be higher. This was a fantastic answer. Thank you for correcting my misconception -- I did not know that the resistance of a motor is constant.
I had a feeling that the batteries were limiting the performance of the motor because they couldn't deliver that much current. Batteries are normally rated in Ampere-hours (Ah), not in Amperes. An Ampere-hour is a measure of the energy stored in the battery, and is not directly related to the current that the battery can deliver.
Batteries also see a decrease in terminal voltage as the output current (load) increases, which also negatively impacts motor speeds at higher torque loads. These factors do not consider the characteristics of the motor winding itself, where output speed decreases as the motor load increases, even with constant battery voltage (see Graph 1, below).
Any guidance you could provide there would also be much appreciated. The battery does not have high enought voltage (3.2V battery vs 40-450 motor), so you need to change the voltage by connecting more such batteries in serie (10 and more), or using some step-up DC/DC change.
An essential criteria in battery selection is making sure that the battery will not only supply the motor’s voltage and current requirements when fully charged, but also continue to meet those requirements as it approaches full discharge.
Adding the third battery will give you a 50% longer run time before the batteries need recharging, but shouldn't change the motor's performance. Adding more batteries in parallel won't cause the motor to draw more current because the voltage remains the same as before.