We consider the Standard Model extended by the addition of a complex scalar singlet, with no assumptions about additional symmetries of the potential. This model provides for resonant di-Higgs production of Higgs particles with different masses. We demonstrate that regions of parameter space allowed by precision electroweak measurements, experimental limits on single Higgs production, and perturbative unitarity allow for large di-Higgs production rates relative to the SM rates. In this scenario, the dominant production mechanism of the new scalar states is di-Higgs production. Results are presented for $\sqrt{S}=13$, $27$ and $100~TeV$.

11 pages, 5 figures; version to be published in Phys. Rev. D, 3 new figures