Currently I have a SINGLE 3 phase connection power supply. I intend to convert it from ONE 3 phase connection to TWO 3 phase connections. Is there a way to do that?
Assuming you mean receptacle, yes you can split a split a three phase branch circuit into multiple receptacles the same way it is done for regular 120V circuits. It's rare though as most three phase machinery draws a lot of power which warrants dedicated circuits. But, if you have a small shop and you only use one machine at a time, then it's fine.
My grandfather had a mini shop inside my fathers shop and he had a single 20A 208V circuit that ran to three twist lock outlets. He had a mill, lathe and surface grinder. All of which could easily share a single circuit because he never ran more than one at a time.
Two long for a comment: A little more information would be helpful. It is possible to have multiple "taps" on the 3 phase supply. Knowing the kind of supply is important is it a delta where 2 legs are the same voltage to ground and the "high leg" is 2x the voltage in the U.S. This is the B phase and is color coded orange. Or is it a wye all 3 legs have the same voltage to ground. The reason I mentioned this is because the equipment needs to have the proper voltage rating for example the disconnect/ breaker on a 480 wye can be 480/277 but a delta requires 480 because of the high leg. With that said you would want to make sure there is a circuit breaker Sized for the new tap conductors and an equipment ground or earth connection of sufficient size. With some more information I can help you size the breaker and wires that would meet U.S. Codes and others could provide local information and code requirements. What we need to help the size of the supply, the size of the additional load, and what is your location.