You would need a second VT.
But not so fast. This is an old post where I tried to debunk most of the popular notions about split-phase:
In my own house I run a 240V Euro type VT and calibrate it down by half for a 120V reference.
What is it that compels you to want to do this? Virtually all IoTaWatt run with a single VT, even most of the three-phase installations, and the overall power monitoring is good. If you think you have some kind of huge imbalance or ground issue, maybe two 120V references would help to diagnose that, but the only way it will increase the accuracy of your most likely dominant 240V loads is if you use two CTs on each of them and assign each to their respective leg. A lot of trouble and expense for marginal, arguably insignificant improvement.
My recommendation would be to try the single 120V reference. If you don’t get satisfactory results, you can add another or better switch to a 240V reference.