We study the process gg --> b (b) over barH(+)H(-) at large tanbeta, where it represents the dominant production mode of charged Higgs boson pairs in a Type II 2-Higgs doublet model, including the minimal supersymmetric standard model. The ability to select this signal would in principle enable the measurements of some triple-Higgs couplings, which in turn would help understanding the structure of the extended Higgs sector. We outline a selection procedure that should aid in disentangling the Higgs signal from the main irreducible background. This exploits a signature made up by "four b-quark jets, two light-quark jets, a tau-lepton and missing energy". While, for beta greater than or similar to30 and over a significant MH+/- range above the top mass, a small signal emerges already at the Large Hadron Collider after 100 fb(-1), ten times as much luminosity would be needed to perform accurate measurements of Higgs parameters in the above final state, rendering this channel a primary candidate to benefit from the so-called "Super" Large Hadron Collider option, for which a tenfold increase in instantaneous luminosity is currently being considered.