If a VFD or any other type of electrical equipment has multiple signals coming into it and it's inputs all have one side (usually the negative) tied together, then you have forced each piece of equipment which is sending a signal in to have the same common. Some signals are referenced to different potentials and when all are tied together, they conflict with each other. You can get unexpectedly high currents or even fuses releasing. If any of the signals have an AC reference to any other signal, the AC may appear in the signal causing even worse problems.
To avoid this, some VFD manufacturers float their multiple inputs and outputs with optic isolators and similar circuitry so this conflict doesn't occur.
If your equipment doesn't float its inputs, then there are devices that will "float" each individual signal. They will be 0-10V in, 0-10V out, 4-20ma in, 4-20ma out, or any other configuration but the important part is that they isolate both sides of the signal from any other reference so they can be attached to an input with a forced reference and no conflict will occur.
I rarely have to use such devices but I think Action Instruments is one source for these. I'm sure if you Google "signal isolator", you will find more.