I am sure there are a lot of special function chips but make sure that the motor can go faster. Usually stepper motors are slower than servos, asynchronus or classic PM motors. No surprise that it skips some steps or even turns back.

On an old application note, I saw a technique to improve every step by doubling or even tripling the voltage driven to the motor with carefully selected coil in series and appropriate current limiting.

But even like that, I don't see a more than 20% increase.

You might want to have a look at the very cheap L297/L298 pair.

Ioannis