  A search for a heavy Higgs boson H decaying into the observed Higgs boson h
with a mass of 125 GeV and another Higgs boson h$_\mathrm{S}$ is presented. The
h and h$_\mathrm{S}$ bosons are required to decay into a pair of tau leptons
and a pair of b quarks, respectively. The search uses a sample of proton-proton
collisions collected with the CMS detector at a center-of-mass energy of 13
TeV, corresponding to an integrated luminosity of 137 fb$^{-1}$. Mass ranges of
240-3000 GeV for $m_\mathrm{H}$ and 60-2800 GeV for $m_\mathrm{h_S}$ are
explored in the search. No signal has been observed. Model independent 95%
confidence level upper limits on the product of the production cross section
and the branching fractions of the signal process are set with a sensitivity
ranging from 125 fb (for $m_\mathrm{H}$ $=$ 240 GeV) to 2.7 fb (for
$m_\mathrm{H}$ $=$ 1000 GeV). These limits are compared to maximally allowed
products of the production cross section and the branching fractions of the
signal process in the next-to-minimal supersymmetric extension of the standard
model.
