  In this article we show that $\mathbb{S}/8$ is an $\mathbb{E}_1$-algebra,
$\mathbb{S}/32$ is an $\mathbb{E}_2$-algebra, $\mathbb{S}/p^{n+1}$ is an
$\mathbb{E}_n$-algebra at odd primes and, more generally, for every $h$ and $n$
there exist generalized Moore spectra of type $h$ which admit an
$\mathbb{E}_n$-algebra structure.
