Stepper motor, do new commands override old ones before they are complete?

360 steps between low and peak. The blue line is the numbers of steps.
This stepper was originally used for this exact purpose. The old controller is burned out and there is no replacement available. I'm simply trying to drive the stepper that was already intended for the system.

PIDs will work better than running averages because I'm attempting to get a single nano to run the entire system, and all of the analog inputs are currently in use as well as a few digital ones. I just can't allow the delay() in the stepper movements because slowing down the inputs would be very very bad for the other things being done.