  We derive the full set of field equations for the Metric-Affine version of
the Myrzakulov gravity model and also extend this family of theories to a
broader one. More specifically, we consider theories whose gravitational
Lagrangian is given by $F(R,T,Q, {\cal T},{\cal D})$ where $T$, $Q$ are the
torsion and non-metricity scalars, ${\cal T}$ is the trace of the
energy-momentum tensor and ${\cal D}$ the divergence of the dilation current.
We then consider the linear case of the aforementioned theory and assuming a
cosmological setup we obtain the modified Friedmann equations. In addition,
focusing on the vanishing non-metricity sector and considering matter coupled
to torsion we obtain the complete set of equations describing the cosmological
behaviour of this model along with solutions.
