  We propose a new non-trivial way to combine mimetic dark matter with the
mimetic formulation of unimodular gravity. This yields a Weyl-invariant
higher-derivative scalar-vector-tensor theory. We demonstrate that on-shell its
behavior mimics GR with an additional k-essence scalar. The overall scale of
the k-essence arises as an integration constant -- a global degree of freedom.
Interestingly, we find that the resulting fluid cannot make transition through
ultra-relativistic equation of state. We develop a method to find a mimetic
theory corresponding to any eligible k-essence and identify, which k-essences
can or cannot be reproduced this way. Finally, we show that abandoning the Weyl
symmetry of the setup allows us to obtain both unimodular gravity and mimetic
dark matter simultaneously, from one conformal redefinition of the metric.
