We investigate the LHC phenomenology of a model where the Standard Model (SM) scalar sector is extended by two real scalar singlets. A $${{\mathbb {Z}}_2} \otimes {{\mathbb {Z}}_2} '$$ $Z_2\otimes {Z_2}^{\prime }$ discrete symmetry is imposed to reduce the number of scalar potential parameters, which is spontaneously broken by the vacuum expectation values of the singlet fields. As a result, all three neutral scalar fields mix, leading to three neutral CP-even scalar bosons, out of which one is identified with the observed Higgs boson at 125 GeV. We explore all relevant collider signatures of the three scalars in this model. Besides the single production of a scalar boson decaying directly to SM particle final states, we extensively discuss the possibility of resonant multi-scalar production. The latter includes decays of the produced scalar boson to two identical scalars (“symmetric decays”), as well as to two different scalars (“asymmetric decays”). Furthermore, we discuss the possibility of successive decays to the lightest scalar states (“cascade decays”), which lead to experimentally spectacular three- and four-Higgs final states. We provide six benchmark scenarios for detailed experimental studies of these Higgs-to-Higgs decay signatures.