  In this paper, we propose a model including four scalar fields coupled with
general gravity theories, which is a generalization of the two-scalar model
proposed in Phys. Rev. D \textbf{103} (2021) no.4, 044055, where it has been
shown that any given spherically symmetric static/time-dependent spacetime can
be realized by using the two-scalar model. We show that by using the
four-scalar model, we can construct a model that realizes any given spacetime
as a solution even if the spacetime does not have a spherical symmetry or any
other symmetry. We also show that by imposing constraints on the scalar fields
by using the Lagrange multiplier fields, the scalar fields become non-dynamical
and they do not propagate. This tells that there does not appear any sound
which is usually generated by the density fluctuation of the fluid. In this
sense, the model with the constraints is a most general extension of the
mimetic theory in JHEP \textbf{11} (2013), 135, where there appears an
effective dark matter. The dark matter is non-dynamical and it does not
collapse even under gravitational force. Our model can be regarded as a general
extension of any kind of fluid besides dark matter. We may consider the case
that the potential of the scalar fields vanishes and the model becomes a
non-linear $\sigma$ model. Then our formulation gives a mapping from the
geometry of the spacetime to the geometry of the target space of the non-linear
$\sigma$ model via gravity theory although the physical meaning has not been
clear. We also consider the application of the model to $f(Q)$ gravity theory,
which is based on a non-metricity tensor and $Q$ is a scalar quantity
constructed from the non-metricity tensor. ...
