  We prove that if $T$ is a complete theory with weak elimination of
imaginaries, then there is an explicit bijection between strict independence
relations for $T$ and strict independence relations for $T^{\text{eq}}$. We use
this observation to show that if $T$ is the theory of the Fra\"{i}ss\'{e} limit
of finite metric spaces with integer distances, then $T^{\text{eq}}$ has more
than one strict independence relation. This answers a question of Adler [1,
Question 1.7].
