  We classify fusion systems $\mathcal{F}$ in which $O_p(\mathcal{F})=\{1\}$,
and there are two $\mathrm{Aut}_{\mathcal{F}}(S)$-invariant essential subgroups
whose normalizer systems generate $\mathcal{F}$. We employ the amalgam method
and, as a bonus, obtain $p$-local characterizations of certain rank $2$ group
amalgams whose parabolic subgroups involve strongly $p$-embedded subgroups.
