  In this work we explore two possible scenarios that can be considered to
extend a recent proposed model by the authors known as reconstructed mimetic
cosmology. This study is complemented with an statistical analysis for each
case. The first scenario considers the inclusion of matter production as a
possible source of cosmic expansion in the reconstructed mimetic model, at
effective level was found that this construction can cross the phantom divide,
the model evolves from quintessence to phantom dark energy. The second scenario
corresponds to a construction of an interacting scheme for the dark sector
which is described by the unified mimetic model. The resulting interaction term
(not imposed by an Ansatz), $Q$, exhibits changes of sign leading to the
violation of the second law along the cosmic evolution and non adiabaticity;
the temperatures for the components of the dark sector are computed and such
components are shown to be out of thermal equilibrium.
