The potential of future analyses to exclude or discover heavy, neutral Higgs bosons is analyzed in the context of models with two Higgs doublets. The production of a heavy scalar H boson and pseudo-scalar $\mathcal{A}$ boson through gluon fusion, with subsequent decay $\mathrm{H}\to \mathrm{ZZ}\to 4\mathrm{\ell}$ ($\ell=\mathrm{e},\mu$) and $\mathcal{A}\to \mathrm{Zh}\to\mathrm{\ell\ell}\mathrm{bb}$, is considered. The sensitivity of these analyses is assessed for a dataset consisting of $\int L\mathrm{dt}=3000$~fb$^{-1}$ of proton-proton collisions at $\sqrt{s}=14$~TeV center of mass energy, collected with an average of 140 pileup interactions per bunch crossing.

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