Something is not right here, or this is a very old system, from back in the days when the NEC did not exist...
Those two statements CANNOT coexist in the same system, at least not now. There may have been a time, long before I ever got in the Electrical Business, when you could have legally fed a 3 phase load from a corner grounded system panel with a 2 pole breaker and a grounded conductor. But that has been illegal for as long as I know now, the code requires that all current carrying conductors have an OCPD on them, and in a corner grounded delta system, a 3 phase load will have current being carried on all 3 conductors, regardless of the fact that one of them is at ground potential. If it was installed prior to that code requirement, it may be grandfathered in, but you will not be able to add any 3 phase circuits to it.
So bottom line, this is going to depend on whether or not the new equipment is 3 phase or single phase (you never said). If it is 3 phase, and the installation is really like this, then legally, you will not be able to add it to that panel.