  In the context of two-Higgs doublet models, we explore the possibility of
searching for heavy Higgs bosons in the $t \bar t Z$ and $t bW$ final states.
We develop realistic analyses strategies and in the case of the $t \bar t Z$
channel provide a detailed evaluation of the new-physics reach at the 14 TeV
LHC. We find that already with an integrated luminosity of $300 \, {\rm
fb}^{-1}$ searches for the $t \bar t Z$ signature can provide statistically
significant constraints at low values of $\tan \beta$ for heavy Higgs masses in
the range from around $450 \, {\rm GeV}$ to $1150 \, {\rm GeV}$. Future
searches for heavy Higgses in the $tbW$ final state are also expected to be
able to probe parts of this parameter space, though the precise constraints
turn out to depend sensitively on the assumed systematics on the shape of the
$t \bar t$ background.
