Searching for new scalar bosons via triple-top signature in $cg \to tS^0 \to tt\bar t$

The alignment phenomenon, that the 125 GeV $h^0$ boson so resembles the Standard Model Higgs boson, can be understood in a two Higgs doublet model without discrete symmetry. New Yukawa couplings $\rho_{tt}$ and $\rho_{tc}$ offer new avenues to discover the extra scalar $H^0$ and pseudoscalar $A^0$. We propose to search for $cg \to tH^0$, $tA^0$ followed by $H^0$, $A^0 \to t\bar t$, $t\bar c$, where same-sign dileptons could be the harbinger, with triple-top, in the signature of three leptons plus three $b$-jets, as confirmation. Discovery could touch upon the origin of baryon asymmetry of the Universe.