  A major open question in the theory of Toeplitz operator on the Bergman space
of the unit disk of the complex plane is to fully characterize the set of all
Toeplitz operators that commute with a given one. In [2], the second author
described the sum $S = T_{e^{im\theta}f} +T_{e^{il\theta}g}$, where $f$ and $g$
are radial functions, that commutes with the sum $T = T_{e^{ip\theta}r(2M+1)p}
+T_{e^{is\theta}r(2N+1)s}$ . It is proved that $S = cT$, where $c$ is a
constant. In this article, we shall replace $r^{(2M+1)p}$ and $r^{(2N+1)s}$ by
$r^n$ and $r^d$ respectively, with $n$ and $d$ in $\mathbb{N}$, and we shall
show that the same result holds.
