  We show that the celebrated Lomonosov theorem cannot be improved by
increasing the number of commuting operators. Specifically, we prove that if T
is the operator on l_1 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.
