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

We advocate two Higgs doublet model without $Z_2$ symmetry, and focus on the extra 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 $cg\to t{A}^0$, $t{H}^0$ can lead to $tt\bar{c}$ same-sign top, or top-assisted di-Higgs $t{h}^0{h}^0$ signatures, resp. As bonus material, we explore the constraint provided by current 4-top search, but advocate direct search for triple-top generated by $cg\to t{H}^0\mathrm{/}{A}^0\to tt\bar{t}$ for $H^0,A^0$ above $t\bar{t}$ threshold, and offer some insight on the mild but intriguing “excess” found by CMS in $gg \to A^0 \to t\bar t$ at 400 GeV.