  We study three different multi-orbital models for iron-based superconductors
(iron-SCs) in the solvable limit of weakly coupled square plaquettes. The
strongest superconducting (SC) pairing is in the $A_{1g}$ $s$-wave channel and
its development is correlated with the emergence of the next-nearest-neighbour
antiferromagnetism (NNN-AFM). For the models with more than three orbitals,
this study suggests that the signs of the intra-orbital pairing order
parameters of the $d_{xy}$ and the $d_{xz}$ (or $d_{yz}$) orbitals must be {\it
opposite}. Such sign difference stems from the intrinsic symmetry properties of
inter-orbital hoppings and might, ultimately, lead to the sign-change of the SC
orders between the hole Fermi pockets at the $\Gamma$ point and produce
anisotropic or even gapless SC gaps in the electron Fermi pockets around the
$M$ point in reciprocal space, as restoring back to the homogeneous limit.
