  Let $\Lambda$ be a finite-dimensional associative algebra over a field. A
semibrick pair is a finite set of $\Lambda$-modules for which certain Hom- and
Ext-sets vanish. A semibrick pair is completable if it can be enlarged so that
a generating condition is satisfied. We prove that if $\Lambda$ is
$\tau$-tilting finite with at most 3 simple modules, then the completability of
a semibrick pair can be characterized using conditions on pairs of modules. We
then use the weak order to construct a combinatorial model for the semibrick
pairs of preprojective algebras of type $A_n$. From this model, we deduce that
any semibrick pair of size $n$ satisfies the generating condition, and that the
dimension vectors of any semibrick pair form a subset of the column vectors of
some $c$-matrix. Finally, we show that no "pairwise" criteria for
completability exists for preprojective algebras of Dynkin diagrams with more
than 3 vertices.
