In several searches for additional Higgs bosons at the LHC, in particular in a CMS search exploring decays to pairs of top quarks, $$t\bar{t}$$
t
t
¯
, and in an ATLAS search studying tau leptons, $$\tau ^+\tau ^-$$
τ
+
τ
-
, local excesses of about $$3\,\sigma $$
3
σ
standard deviations or above have been observed at a mass scale of approximately $$ 400 \,\text {GeV}$$
400
GeV
. We investigate to what extent a possible signal in these channels could be accommodated in the Next-to-Two-Higgs-Doublet Model (N2HDM) or the Next-to Minimal Supersymmetric Standard Model (NMSSM). In a second step we analyze whether such a model could be compatible with both a signal at around $$400\,\text {GeV}$$
400
GeV
and $$96\,\text {GeV}$$
96
GeV
, where the latter possibility is motivated by observed excesses in searches for the $$b \bar{b}$$
b
b
¯
final state at LEP and the di-photon final state at CMS. The analysis for the N2HDM reveals that the observed excesses at $$400 \,\text {GeV}$$
400
GeV
in the $$t\bar{t}$$
t
t
¯
and $$\tau ^+\tau ^-$$
τ
+
τ
-
channels point towards different regions of the parameter space, while one such excess and an additional Higgs boson at around $$96\,\text {GeV}$$
96
GeV
could simultaneously be accommodated. In the context of the NMSSM an experimental confirmation of a signal in the $$t\bar{t}$$
t
t
¯
final state would favour the alignment-without-decoupling limit of the model, where the Higgs boson at $$125\,\text {GeV}$$
125
GeV
could be essentially indistinguishable from the Higgs boson of the standard model. In contrast, a signal in the $$\tau ^+\tau ^-$$
τ
+
τ
-
channel can only be accommodated outside of this limit, and parts of the investigated parameter space could be probed with Higgs signal-rate measurements at the (HL-)LHC.