  Motivated by the fact that septuple-atomic-layer MnBi$_2$Te$_4$ can be
structurally viewed as the combination of double-atomic-layer MnTe
intercalating into quintuple-atomic-layer Bi$_2$Te$_3$, we present a general
approach of constructing twelve septuple-atomic-layer $\alpha_i$- and
$\beta_i$-$MA_2Z_4$ monolayer family (\emph{i} = 1 to 6) by intercalating
MoS$_2$-type $MZ$$_2$ monolayer into InSe-type A$_2$Z$_2$ monolayer. Besides
reproducing the experimentally synthesized $\alpha_1$-MoSi$_2$N$_4$,
$\alpha_1$-WSi$_2$N$_4$ and $\beta_5$-MnBi$_2$Te$_4$ monolayer materials,
another 66 thermodynamically and dynamically stable $MA_2Z_4$ were predicted,
which span a wide range of properties upon the number of valence electrons
(VEC). $MA_2Z_4$ with the rules of 32 or 34 VEC are mostly semiconductors with
direct or indirect band gap and, however, with 33 VEC are generally metal,
half-metal ferromagnetism, or spin-gapless semiconductor upon whether or not an
unpaired electron is spin polarized. Moreover, we propose
$\alpha_2$-WSi$_2$P$_4$ for the spin-valley polarization,
$\alpha_1$-TaSi$_2$N$_4$ for Ising superconductor and $\beta_2$-SrGa$_2$Se$_4$
for topological insulator.

Materials Science