Hmmmmmm
You could trip an overcurrent without hitting 2.2kW if you were going under the rated motor speed. The current is proportional to (torque - losses), and the rating on a motor is not a hard limit. A 0.6Nm motor could produce 0.7Nm for example, but the current rise from 0.6-0.7Nm might be double that from 0.5-0.6Nm due to saturation effects. Basically the iron is starting to become less of a magnetic conductor and so your magnetic resistance (called Reluctance) goes up and more magnetic field strength (like the magnetic voltage) is required to push more total flux (like the magnetic current) through the iron.
Torque is exactly the cross product of the current through the field times the radius about center of rotation in the plane of rotation this occurs at. That's the portion of the electrical current that is perpendicular to the field AND tangent to the circle of rotation.
Long story short, you can always pump more current into a motor and trip your overcurrent. If you are looking for HP you have to run at or just under the rated speed to max it out. If you have a VFD with vector control and field weakening in most but not all motors, about 5% past the rated speed will allow for the highest power due to higher efficiency. A 3kW VFD might be able to run that 2.2kW spindle at say, 2.3kW at that point.
The practical issue there is if you hit your torque limit on the spindle it will slow down and likely overcurrent, so you have to run it under max power.
Also keep in mind that for short durations the spindle can run at something like 200% rated torque and power, but it will overheat.