Generalizing results from $[\text{MM}1]$ referring to the intersection body $\text{IK}$ and the cross-section body $CK$ of a convex body $K\,\,\subset \,\,{{\mathbb{R}}^{d}}$, $d\,\ge \,2$, we prove theorems about maximal $k$-sections of convex bodies, $k\,\in \,\{1,\,\ldots ,\,d\,-\,1\}$, and, simultaneously, statements about common maximal $(d\,-\,1)-$ and 1-transversals of families of convex bodies.