A search is presented for additional neutral Higgs bosons in the di-$\tau$ final state in pp collisions at the LHC. The search is performed in the context of the minimal supersymmetric extension of the standard model (MSSM), on the data collected with the CMS detector in 2016 at a center-of-mass energy of 13~\mathrm{TeV}, corresponding to an integrated luminosity of 35.9~\mathrm{fb}^{-1}. To enhance the sensitivity to neutral MSSM Higgs bosons the search includes the case where the Higgs boson is produced in association with b quarks. No significant deviation above the expected background is observed. Model-independent limits are set on the product of the cross section and branching fraction for the production via gluon-fusion or in association with b quarks. These limits range from 18~\mathrm{pb} (at 90~\mathrm{GeV}) to 3.5\times 10^{-3}~\mathrm{pb} (at 3.2~\mathrm{TeV}) for gluon-fusion and from 15~\mathrm{pb} (at 90~\mathrm{GeV}) to 2.5\times 10^{-3}~\mathrm{pb} (at 3.2~\mathrm{TeV}) for b-associated production. In the $m_{\text{h}}^{\text{mod+}}$ scenario these limits translate into an exclusion of $\tan\beta>6$ for m_{\text{h}}\lesssim 200~\mathrm{GeV}. The exclusion contour ranges up to 1.6~\mathrm{TeV} for $\tan\beta<60$.

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