A study of two-Higgs-doublet models (2HDM) in the decoupling limit reveals the existence of parameter configurations with a large triple-Higgs self-coupling as the only low-energy trace of the departure from a Standard Model (SM) Higgs sector. This observation encourages attempts to search for double Higgs production at the Large Hadron Collider (LHC) even in mass regions which have been shown to be very hard to probe in the context of SM-like Higgs self-couplings. In this document we consider the case of an Intermediate Mass Higgs (IMH) boson, with 120 GeVMH140 GeV, produced in pairs via vector-vector fusion, Higgs-strahlung and associate production with heavy-quarks and decaying into b pairs. After a detailed signal-to-background analysis, we confirm that the observation of a Higgs-pair signal is very challenging in the framework of the SM, even at the LHC with upgraded luminosity. In contrast, we verify that the sensitivity is sufficient to detect departures from the SM which would escape detection in the measurements of the single-Higgs production channels.