OK, we need to know the make and model of your mill, the current highest spindle speed and the rated speed and power of the motor currently fitted.
You cannot (easilly, someone will aways argue) run a capacitor start (centrifugal switch operated) motor at significantly higher than rated speed. You can possibly go 20% higher as most motors, or at least their parts, are designed for 50 or 60 Hz.
We can give better guidance knowing the above but basically your choices are:
1/ Fit a 3 phase ac motor and VFD this is probably the best option but depends on the mill and in particular if the spindle (and any gears) will run at 4000 RPM.
2/ Fit a separate high speed spindle carried in the existing spindle. No modification to mill and as fast as you like. Reduces clearance over table but may not be an issue for your work.
3/ Fit a different tyype of motor e.g. a universal or BLDC (as mentioned by Peter) but these will need more work and may not be as good for other work. spindle speed limitaions still apply.
Robert.