Hello.
You might be able to use our MC33926 Arduino shield to drive your stepper motor. You can find sample code for using the shield as a stepper motor driver in this post.
I do not recommend using multiple H-bridges in parallel. In general, it is tricky to parallel things, and if the timing for turning off and on the MOSFETs is not precise, you might unintentionally have shoot-through that could damage the driver. Also, it is not clear to me what you mean by “current level shifters”.
- Jeremy