  Conformal and disformal transformations are now being very intensively
studied in the context of various modified gravity theories. In particular,
some special classes of them can be used for constructing Mimetic Dark Matter
models. Recently, it has been shown that many more transformations of this
type, if not virtually all of them when the coefficients depend on the scalar
kinetic term, can produce new solutions with mimetic properties. The aim of
this paper is to explain how it works at the level of the variational
principle, and to express some worries about viability of these models.
