We consider search strategies for an extended Higgs sector at the high-luminosity LHC14 utilizing multi-top final states. In the framework of a Two Higgs Doublet Model, the purely top final states ($tbar t, , 4t$) are important channels for heavy Higgs bosons with masses in the wedge above $2,m_t$ and at low values of $tanbeta$, while a $2 b 2t$ final state is most relevant at moderate values of $tan beta$. We find, in the $tbar t H$ channel, with $H rightarrow t bar t$, that both single and 3 lepton final states can provide statistically significant constraints at low values of $tan beta$ for $m_A$ as high as $sim 750$ GeV. When systematics on the $t bar t$ background are taken into account, however, the 3 lepton final state is more powerful, though the precise constraint depends fairly sensitively on lepton fake rates. We also find that neither $2b2t$ nor $t bar t$ final states provide constraints on additional heavy Higgs bosons with couplings to tops smaller than the top Yukawa due to expected systematic uncertainties in the $t bar t$ background.
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