I would be quite sure that the designers of the machine took into account the speed attainable, commensurate with extended bearing life. Any speeds excessive to the design are likely to reduce the life of the bearings, but a safety factor will/should have been used in the design.
That means any increase will initially eat into the ‘safety net’ included in the design. Likely 20-50%, but after that bearings may either a) wear significantly faster or b) risk failing.
So, I would guess you might get away with 20%. Increase, but then with no safety margin – and that would depend on how loaded the bearings might be, in use, and their initial condition.
There may be other parts of the machine which could fail if excessive speeds are used. Like doubling the rotational speed of a chuck might put it beyond its design safety factor (although most chucks will be rated above 2000rpm, I expect).
Motors are often capable of much higher speeds, but they are likely well balanced and have high speed ball bearings fitted, which are easly replaced, as service items.