Simple problem to fix. Whenever one motor is running and they want to start the other, just stop the first and start both together.
That might actually work if the ramp up needs for both motors are similar enough.
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That is the way it is done, yes.
One caveat though, you will need to assure that the first motor is STOPPED before re-starting. VFDs can do what is called "Flying Restart", that catches a an already spinning motor on the fly, matches its speed and accelerates it from there. But only into ONE motor; trying it with 2 motors can create a situation where they are at different speeds, so like generators out of synch, can create a nasty voltage spike that also takes out the transistors.
More common in a situation like this is to have a contactor arrangement on the output that uses the VFD to ramp one motor to full speed, then it is transferred to an Across-the-Line starter. The VFD is then "recycled" for the 2nd motor.
Another way to do this is what's called a "common DC bus" arrangement that, instead of having one big drive capable of both motors, have one rectifier, but two smaller inverters connected to it, one to each motor. They can then run independently of each other, but any regen from one is used in the other.
Both of those last two options however would have needed to have been engineered into the system up front. it sounds as if this drive already exists. In that case, your only option is what GoldDigger said; shut it down, add in the 2nd motor once the first one is stopped, then re-start.
