Typical motors may have a voltage rating of perhaps 2 to 5 volts, however that may not be the actual voltage at which the motors are operated. Normally the driver used with such motors applies a higher voltage than the rated voltage, but regulates the current (for example, through "chopping" of the power supplied to the motor) to keep the current within the motor's rating.
For example, this 4-wire motor has a 2.55 volt rating and has a holding torque of 381 oz-in (which is substantially more torque than you will find in a NEMA 17 size motor):
Also, this 8-wire motor has different voltage ratings depending on the hookup type, ranging from 1.93 to 3.86 volts, with a holding torque ranging from 200 to 282 oz-in:
So, while I do not know what type of driver you are using, my guess is that if you are driving NEMA 17 motors at 12 volts with it, then it is a type of driver that is performing current limiting, and you should be able to drive a NEMA 23 motor with it. The question that will arise, however, is how much current your driver is designed to deliver compared with the current rating of the motor that you intend to use with it. If your driver can not supply sufficient current to the motor, then you will not achieve the ultimate torque that the motor is capable of providing.
As far as voltage, using a higher voltage than 12 volts would permit your motor to achieve higher torque at higher speeds. The inductance of the motor winding is also a factor that affects the ultimate motor speed based on the supplied voltage. However your question said nothing about speed, rather your concern was about torque.