  A system $\mathcal M$ of equivalence relations on a set $E$ is
\emph{semirigid} if only the identity and constant functions preserve all
members of $\mathcal M$. We construct semirigid systems of three equivalence
relations. Our construction leads to the examples given by Z\'adori in 1983 and
to many others and also extends to some infinite cardinalities. As a
consequence, we show that on every set of at most continuum cardinality
distinct from $2$ and $4$ there exists a semirigid system of three equivalence
relations.
