We investigate the discovery prospects for NMSSM Higgs bosons during the
13~TeV run of the LHC. While one of the neutral Higgs bosons is demanded to
have a mass around 125~GeV and Standard Model (SM)-like properties, there can
be substantially lighter, nearby or heavier Higgs bosons, that have not been
excluded yet by LEP, Tevatron or the 8~TeV run of the LHC. The challenge
consists in discovering the whole NMSSM Higgs mass spectrum. We present the
rates for production and subsequent decay of the neutral NMSSM Higgs bosons in
the most promising final states and discuss their possible discovery. The
prospects for pinning down the Higgs sector of the Natural NMSSM will be
analysed taking into account alternative search channels. We give a series of
benchmark scenarios compatible with the experimental constraints, that feature
Higgs-to-Higgs decays and entail (exotic) signatures with multi-fermion and/or
multi-photon final states. These decay chains furthermore give access to the
trilinear Higgs self-couplings. We briefly discuss the possibility of
exploiting coupling sum rules in case not all the NMSSM Higgs bosons are
discovered
