Don't think of it as two different machines, but rather, two different power supplies. A machine can have multiple power supplies, so we are all assuming that you have 1 power supply per machine. Also, we are assuming that both power supplies are the same input and output voltages.
Each machine sending one signal to one input module. So each of those signals is ultimately coming from one power supply, so those commons can be tied together as long as output voltages from each power supply are the same. I'm unaware if the max current from each power supply has any affect, maybe someone else can clarify. I just know as long as output voltages are the same, then combining those commons together should be ok.