Ok, my input...
I have a VFD driving a 3-speed motor, with an interlock on the 3-speed switch that disables the VFD output (GATE BLOCK input), works well. Most VFDs nowadays can be configured with two or more sets of motor parameters, so if the full-load amps is different for the speeds amother microswitch can select appropriately. On mine the currents are close enough to get away with a single set, YMMV.
An alternative is to stick to one motor speed and use.the VFD as.a.continuous speed.controller, usually the low.speed winding will deliver more torque, so perhaps run that to.a.higher frequency? I run my 4/6/8 pole motor up to 80Hz (50 standard) connected as 4-pole, to get my lathe's spindle speed.up to 2500 rpm for *short* periods, more from sympathy for the headstock plain bearings than the motor - the BTH motor's finely balanced.and can take it (and a.coin on edge balances on the headstock at 2500...)
Dave H. (the.other one)