In extended Higgs sectors that exhibit alignment without decoupling, the additional scalars are allowed to have large couplings to the Standard Model Higgs. We show that current nonresonant di-Higgs searches can be straightforwardly adapted to look for additional Higgses in these scenarios, where pair production of non-SM Higgses can be enhanced. For concreteness, we study pair production of exotic Higgses in the context of an almost inert two Higgs doublet model, where alignment is explained through an approximate $mathbb{Z}_2$ symmetry under which the additional scalars are odd. In this context, the smallness of the $mathbb Z_2$ violating parameter suppresses single production of exotic Higgses, but it does not prevent a sizeable trilinear coupling $hHH$ between the SM Higgs ($h$) and the additional states ($H$). We study the process $pprightarrow h^* rightarrow HH$ in the final states $bbar b b bar b$, $bbar bgammagamma$, and multi-leptons. We find that at the HL-LHC these modes could be sensitive to masses of the additional neutral scalars in the range $130mbox{ GeV} lesssim m_H lesssim 290mbox{ GeV}$.
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