  The worldline of a spinning test body moving in curved spacetime can be
provided by the Mathisson-Papapetrou-Dixon (MPD) equations when its centroid,
i.e. its center of mass, is fixed by a Spin Supplementary Condition (SSC). In
the present study, we continue the exploration of shifts between different
centroids started in a recently published work [ Phys. Rev. D 104, 024042
(2021)], henceforth Paper I, for the Schwarzschild spacetime, by examining the
frequencies of circular equatorial orbits under a change of the SSC in the Kerr
spacetime. In particular, we examine the convergence in the terms of the
prograde and retrograde orbital frequencies, when these frequencies are
expanded in power series of the spin measure and the centroid of the body is
shifted from the Mathisson-Pirani or the Ohashi-Kyrian-Semerak frame to the
Tulczyjew-Dixon one. Since in Paper I, we have seen that the innermost stable
circular orbits (ISCOs) hold a special place in this comparison process, we
focus on them rigorously in this work. We introduce a novel method of finding
ISCOs for any SSC and employ it for the Tulczyjew-Dixon and the
Mathisson-Pirani formalisms. We resort to numerical investigation of the
convergence between the SSCs for the ISCO case, due to technical difficulties
not allowing Paper's I analytical treatment. Our conclusion, as in Paper I, is
that there appears to be a convergence in the power series of the frequencies
between the SSCs, which is improved when the proper shifts are taken into
account, but there exists a limit in this convergence due to the fact that in
the spinning body approximation we consider only the first two lower multipoles
of the extended body and ignore all the higher ones.
