How do you try to accelerate your stepper? Do you made your own sketch? Do you use a firmware like Marlin or Teacup?
The standard polulu A4988 can have a maximum of 500kHz. With well programmed firmware and a modern controller this is possible. Just reached 525kHz with Teacup on a STM32F411 at 108MHz.
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the_digital_dentist
You can't get a stepper to go that fast, even with no load. You'll need a different type of motor.
You can do full steps with that driver, but at 2000 rpm you need 400k steps per second. I don't think the driver can keep up with that pulse rate.
If you need precision and speed like that you need to look at servo motors and drivers.
The standard polulu A4988 can have a maximum of 500kHz. With well programmed firmware and a modern controller this is possible. Just reached 525kHz with Teacup on a STM32F411 at 108MHz.