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We advocate two Higgs doublet model without $Z_2$ symmetry, and focus on theextra top Yukawa couplings $\rho_{tt}$ and $\rho_{tc}$. We show that $A^0$ and$H^0$ bosons are still allowed at 300 GeV mass, where $cg \to tA^0$, $tH^0$ canlead to $tt\bar c$ same-sign top, or top-assisted di-Higgs $th^0h^0$signatures, resp. As bonus material, we explore the constraint provided bycurrent 4-top search, but advocate direct search for triple-top generated by$cg \to tH^0/A^0 \to tt\bar t$ for $H^0,\, A^0$ above $t\bar t$ threshold, andoffer some insight on the mild but intriguing "excess" found by CMS in $gg \toA^0 \to t\bar t$ at 400 GeV.

Top-Higgs Associated Production involving {\boldmath ${A^0},\, {H^0}$} with Mass at 300 GeV