  We prove that for given $k\in\mathbb{N}$, $k\geq 3$, $d\in\mathbb{N}$ and
each $a\in\mathbb{R}^{*}$ with \begin{align*} a^2\leq 4d (d+k-2)(k-2)^{-2}
\end{align*} the ellipsoid
$E_a:=\{x\in\mathbb{R}^k\,\lvert\,a^{-2}x_1^2+x_2^2+\ldots+x_k^2=1\}$ admits
infinitely many harmonic self-maps.
