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

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 $cg\to t{H}^0$, $t{A}^0$ 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.