Yes they exist. I use them in a project that can run on 12v or 24 v . parallel on 12 v and series on 24 to reduce current draw.
A four lead motor must be bipolar . There are other proprietary designs as well that use 5 or 7 wires but thoes motors are usually complete with an integral driver.
There is a lot more to extracting the performance from step motors than just the step sequence and ramp rates. Terry