  The most general renormalizable interaction between the Higgs sector and a
new gauge-singlet scalar $S$ is governed by two interaction terms: cubic and
quartic. The quartic interaction is only loosely constrained by invisible Higgs
decays. Given current experimental limits about $10\%$ of all Higgs bosons
created at the LHC can be converted to new scalars with the mass up to $m_{\rm
Higgs}/2$. This can significantly extend the reach of the LHC-based Intensity
Frontier experiments. We analyze the sensitivity of the FASER experiment to
this model and discuss modest changes in the FASER 2 design that would allow to
explore an orders-of-magnitude wider part of the Higgs portal's parameter
space.
