  We show how effects of compositeness emerging in a Composite 2-Higgs Doublet
Model can enter Standard Model (SM)-like Higgs pair production at the Large
Hadron Collider in both resonant and non-resonant mode. Such effects can arise
from modified trilinear Higgs self-couplings and top-Yukawa couplings as well
as from loops of new heavy quarks and additional quartic Higgs-fermion
interactions. In the resonant case, significant distortions of the Breit-
Wigner shape of a new scalar state decaying into the two SM-like Higgs states
may occur due to interference effects amongst not only the SM-like diagrams but
also those involving the new heavy quarks. In the non-resonant case, a
modification of the underlying line-shape and a local maximum at twice a new
heavy quark mass appear simultaneously. We quantify these effects by taking
into account the relevant theoretical and latest experimental bounds.
