At least there are enough connections... but it still depends on how the cabling is done within the headphone. You could ask Shure support on how the connectors are used on that jack. If +/- of both drivers are completely independent, a balanced cable could be manufactured (or maybe someone already builds one) for this use case. But careful, don't try with just any balanced cable: if it doesn't fit with the internal cabling of the headphone, your amp might get damaged.
But again: in all probability you don't need a balanced connection. It's not automatically better and in many cases just provides more power. Which might help with some hard to drive planar magnetic systems, but most probably not in this case. Balanced is no secret sauce (even if some proponents want to make you believe just that).