  The charge transfer compound (BEDT-TTF)$_2$Ag(CF$_3$)$_4$(TCE) crystallizes
in three polymorphs with different alternating layers: While a phase with a
$\kappa$ packing motif has a low superconducting transition temperature of
$T_c=2.6$ K, two phases with higher $T_c$ of $9.5$ and $11$ K are multi-layered
structures consisting of $\alpha'$ and $\kappa$ layers. We investigate these
three systems within density functional theory and find that the $\alpha'$
layer shows different degrees of charge order for the two $\kappa$-$\alpha'$
systems and directly influences the electronic behavior of the conducting
$\kappa$ layer. We discuss the origin of the distinct behavior of the three
polymorphs and propose a minimal tight-binding Hamiltonian for the description
of these systems based on projective molecular Wannier functions.
