I also agree that we seem to be considering two possibilities.
One, where there are cables in parallel, the installation of a magnetic circuit encircling only part of the conductors may make a noticible difference.
Two, encircling one phase of a three phase circuit with a magnetic circuit will have the effect of adding a small amount of impedance to the conductor in question. This effect may not be noticable but it may be measurable, as Gunnar proposes, with .
In the field, we are not usually concerned with the affect of a clamp meter on one phase. We do consider the small effect of a clamp meter around one of a group of parallel conductors. This effect is small but it may be noticable.
As Gunnar pointed out, it may be measured with a DMM.
Greg, the increased inductance in one cable of a parallel run of cables diverts current to the other cables. The heat due to the increased current is developed over the length of the other cables into which the extra current is diverted.
respectfully