A second light Higgs boson, with mass ≈ 140-145 GeV, is predicted by non-minimal Supersymmetric models. This new particle can account for ∼ 3σ excesses recorded by the ATLAS and CMS experiments at the Large Hadron Collider (LHC) during Run 1. We show how this can be explained in a particular realisation of these scenarios, the (B − L) Supersymmetric Model (BLSSM), which also has other captivating features, like offering an explanation for neutrino masses and releaving the small hierarchy problem of the Minimal Supersymmetric Standard Model (MSSM).In the absence of any new physics signal at the LHC above and beyond the Standard Model (SM), as it is presently the case, it has become all the more important to understand the true nature of the Higgs boson discovered in 2012. In fact, as we shall argue below, there is no need to assume that Nature prefers the minimal version of the Higgs mechanism for mass generation. Upon dismissing this assumption, alongside precision measurements of the 125 GeV resonance, it becomes equally important to pursue the search for additional Higgs boson states. In the attempt to discern which amongst the models providing these is the true one, we believe that guidance should be taken from data. While rumours of potential heavy Higgs resonances at ∼ 750 GeV are pervading the collider physics world, based on ∼ 3σ excesses seen by both ATLAS and CMS, we would like to note here that comparable hints for a 140 GeV or so additional Higgs state have been recorded on data by both collaborations with a similar level of significance and, quite crucially, not only in γγ final states (as is the case for the 750 GeV anomaly), but also in the (more precise) ZZ * channel. It is our purpose here to provide a unified solution to the 125 GeV discovery and 140 GeV anomaly in a next-to-minimal Supersymmetric model, which, other than inheriting the well known benefits of Supersymmetry (SUSY), can also boast theoretical attractiveness well beyond the Higgs sector. Should a 140 GeV signal be finally confirmed by additional data, Higgs physics would be drastically advanced in the direction of pointing to non-minimal realisations of SUSY. But, let us proceed in steps.The paradigm that particle physics is minimalist in Nature, at least as far as Electro-Weak Symmetry Breaking (EWSB) goes [1], may simply be the result of early appearance if one realises that the Standard Model (as we know it) appeared to be so initially, but then it revealed itself rather more articulated than we thought or hoped. As for its interactions, there was first the photon, uncharged and massless. We later discovered its massive weak companions, Z and W ± , the latter being charged too. Even the gluon is one of eight, actually. Concerning matter, the story started with one generation of quarks and leptons/neutrinos, that was sufficient to keep our world stable. Then somebody ordered the muon [2] and all apparently fell apart. With it also came its neutrino (not that we saw it at the time or even now). Strangely yet charmingly, t...