  In this work we study the maximum relative diameter functional $d_M$ in the
class of multi-rotationally symmetric planar convex bodies. A given set $C$ of
this class is $k$-rotationally symmetric for
$k\in\{k_1,\ldots,k_n\}\subset\nn$, and so it is natural to consider the
standard $k_i$-partition $P_{k_i}$ associated to $C$ (which is a minimizing
$k_i$-partition for $d_M$ when $k_i\geq3$) and the corresponding value
$d_M(P_{k_i})$. We establish the relation among these values, characterizing
the particular sets for which all these values coincide.
