The ABC-equation revisited: missed (quasi) integrable cases. Part II: extensions and actions

We continue here the study of the $\text{textsc}ABC$-equation $A{u}_x{u}_{yt}+B{u}_y{u}_{xt}+C{u}_t{u}_{xy}=0$, $A$, $B$, $C\in \mathbb{R}$ and using the results obtained in the first part construct new quasi-integrable structures and compute their actions on symmetries and cosymmetries.