I have done this quite a few times. As stated, it the capacitor value you have to juggle around with.
You need a large capacitor value to get the motor up to speed, I use two distinctive groups ,in parallel for starting, then one group (the start group larger in value ) is disconnected, leaving the smaller group (the run group) in circuit. I use two contactors to do the switching. Pressing the start push, count five or pause brings in both contactors and connects both lots of capacitors to the mains and the motor, then release the push and the motor runs. The contactors are so wired as to give no volt release should there be a mains failure and there is a local stop push. Ex fluorescent light capacitors are OK for this application as are ex power factor correction capacitors. Please be extra cautious when handling capacitors of this quality, they can store charge of energy for a time if not fitted with a discharge resistor. I suggest you switch off, wait a while, then short out the terminal of the capacitors with an old screw driver before working on or connecting them. Belts and braces. For coolant pumps I found one small capacitor to be enough as it starts off load in effect. Actually it best to test all three phases with a volt meter and that way one can adjust the capacitor value to get near balance, also put your hand on the motor after its been running for a while, bearing in mind that modern motors run very hot. Ted