A modification of the iterative method of B\"orsch--Supan type for the simultaneous inclusion of polynomial zeros is considered. The modified method provides the simultaneous inclusion of $k$ (of $n\geq k$) zeros, dealing with $k$ inclusion disks of these zeros and the point (unchangeable) approximations to the remaining $n-k$ zeros. It is proved that the $R$-order of convergence of the considered method is two if $k<n$ and three if $k=n$. Three numerical examples are given to illustrate convergence properties of the presented method.