I remember (1970's) working for the county council on portable traffic lights, they had just brought out vehicle sensed traffic lights, with microwave detectors (RADAR) to see when a car was waiting, they came supplied with Peak RADAR however these were proving too sensitive and waving trees were setting off the traffic lights, so they were changed for Mullard and I fitted the new heads, tested in the depot, and all worked A1, took to the site, and they did not work when powered from generator, returned to depot and all A1.
As a young lad I was baffled as to why OK in depot, but failed on site, some phone calls and it turned out the Mullard actually used the centre tap of the 110 volt supply, and the generators did not have a centre tap, so I had to fit a auto transformer to generate the centre tap, talking to my boss he said that's no good, it should not use any power from centre tap, as if the 7 core cable is damaged then it can make the traffic light head live to 55 volt, and it only takes 25 volt to kill a cow.
So the auto transformer needed fitting in the heads, all the Mullard heads were returned and modified. This of course is still the case, TN-C is very limited as to where it can be used, so even if we have centre tap, unless using 4 core cable, we can't use the centre tap.
As to using a 400 volt supply (2 phase) yes have seen many times 400 to 230 volt transformers used because there is no neutral supplied to the machine, I have never seen with split phase (460 volt) a transformer used to step down to 230 volt, always used one phase. I think for a domestic supply (to a premises in the charge of an ordinary person) one is limited to 125 amp, in real terms 100 amp, so if the user needs more than 100 amp, then need to have multi supplies, be it two or three phases, or split phase, would depend on local supply and transformer, so common to find a farm with split phase supply one to farm buildings and one to house. You can have a domestic 3 phase supply with 100 amp per phase, but not a 300 amp supply, as you need type tested distribution units called consumer units which can't be over 125 amp each. I have fitted a three phase switched fuse with 3 x 100 amp fuses, one to each of three consumer units, and all three fuses came off same supply, not sure if this complied?
However other than using a capacitor to start, not seen a two phase motor, and since twin supplies in this country are often split phase rather than two phases from a three phase supply, to build a machine using a two phase motor would be asking for problems.