Special equivalent key in symmetric encryption

Let $k$ and $k'$ be two keys of symmetric encryption such that for some $m$ we have $Enc_k(m)=Enc_{k'}(m)$. Is it possible to exist a plain text $m'$ such that $Enc_k(m') \neq Enc_{k'}(m')$.

In fact, is there exist a key which be equivalent only for special plain text?