Lomonosov's theorem cannot be extended to chains of four operators

We show that the celebrated Lomonosov theorem cannot be improved by increasing the number of commuting operators. Specifically, we prove that if $T\colon\ell _1\to \ell _1$ is the operator without a non-trivial closed invariant subspace constructed by C. J. Read, then there are three operators $S_1$, $S_2$ and $K$ (non-multiples of the identity) such that $T$ commutes with $S_1$, $S_1$ commutes with $S_2$, $S_2$ commutes with $K$, and $K$ is compact. It is also shown that the commutant of $T$ contains only series of $T$.