We present a study of triple Higgs boson (3H) production at the International Linear Collider (ILC) within the general Two-Higgs-Doublet Model (2HDM). We compute the production cross-sections at the leading-order for the 3H final states and find values up to sigma ~ 0.1 pb. This result represents a large enhancement with respect to the corresponding MSSM cross-sections, which stay typically at the level of sigma ~ 10^(-6) pb or less. Furthermore, since the 3H cross-sections in the general 2HDM can be of the order of the double Higgs production cross-sections, such 3H processes could be a competitive (if not the dominant) mechanism for Higgs boson production at the ILC. In practice, these 3H events could be identified through the tagging of 6 heavy-quark jet final states and, in this case, they would provide strong evidence of an extended Higgs boson sector -- likely of non-supersymmetric nature.
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