Can I use one 3-phase circuit to power 2 separate machines?
I can't comment on whether your code has anything specific to say about this but looking at this from a generic safety/functionality point of view.

The currents in each shared live conductor will partially but not completely cancel.

Assuming the loads are resistive, the currents to the loads are 60 degress out of phase, so assuming the loads are equal the total current in each shared live conductor is.

23A * 2 * cos(30°) = 39.8A

If the loads are non-resistive then the calculation gets more complex but 40A is probably still in the right ballpark. AIUI with the way American breakers are rated, if these loads count as "continuous" then that would require a 50A breaker.

The main question IMO is are the appliances suitable for connection to a 50A breaker? or do they require a 30A breaker to operate safely? In the latter case it would seem you need a subpanel.