  We assess the current state of searches at the LHC for additional Higgs
bosons in light of both direct limits and indirect bounds coming from coupling
measurements of the Standard Model-like Higgs boson. Given current constraints,
we identify and study three LHC searches that are critical components of a
comprehensive program to investigate extended electroweak symmetry breaking
sectors: production of a heavy scalar or pseudoscalar with decay to $t \bar t$;
$b \bar b$ and $t \bar t$ associated production of a heavy scalar or
pseudoscalar with decay to invisible final states; and $t \bar b$ associated
production of a charged Higgs with decay to $\bar t b$. Systematic experimental
searches in these channels would contribute to robust coverage of the possible
single production modes of additional heavy Higgs bosons.
