Controls are most often single-phase, although the remainder of the machine may be three-phase.
Identify which of the three incoming phases are connected to the controls. You will most likely see a control transformer connected between two of the three incoming phases, very often A and C.
Now, to make 600 volts three-phase from 240 volts single-phase (or 575 volts three-phase from 230 volts single-phase, or 550 volts three-phase from 220 volts single-phase), you can first make 240 volts three-phase (or 230 volts three-phase, or 220 volts three-phase) and then transform that to 600 volts (or 575 volts, or 550 volts) using a three-phase transformer, OR you can transform that to 600 volts (or 575 volts, or 550 volts) using a single-phase transformer and then make 600 volts (or 575 volts, or 550 volts) three-phase .
Both methods have been successfully employed.
In order to "scale" a 240 volt design to, say, 600 volts, you must adjust the capacitances by the factor (240 / 600) ^ 2 = 0.16. That is, if a 240 volt "reference design" states 100 µF, then for a 600 volt design 16 µF would be required, instead.
As always, the starting capacitor must be rated for the applied voltage, 600, while the running capacitor or the power factor correcting capacitor must be rated for the peak voltage plus a safety factor, 1.56 * 600 = 933.
Coming up with capacitors rated 933 volts will prove to be problematic, but two identical 600 volt capacitors in series give a capacitor rated 1200 volts, but one-half the capacitance.
Any switchgear on the 600 volt side must be rated for "600 volt class". The normal class, "300 volt class", is used for 240 (or 230, or 220) volts.