We analyze the two-orbital (with d x 2 −y 2 and d 3z 2 −r 2 orbitals) analogue of the t-J-U model as applied to the description of the copper-oxide monolayer deposited on the Bi2Sr2CaCu2O 8+δ substrate (CuO2/BSCCO). We show, that an extended s-wave superconducting dome appears in the heavily hole overdoped regime of the model, with dominant contribution to the pairing coming from the d 3z 2 −r 2 orbitals. Also, the lower critical doping for the appearance of the SC state concurs with the Lifshitz Transition after which the hole-like Fermi pockets are created around the M points in the Brillouin zone. The obtained results are in accord with the recent experimental result [cf. Y. Zhong et al., Sci. Bull. 61, 1239]. An analogous two-band description is also analyzed in the context of the Ba2CuO4−y bulk compound, where the heavily hole-overdoped situation is believed to be reached [cf. W. M. Li et al. PNAS 116, 12156 (2019)]. As we show, a two dome structure can be realized in such system with the d-and s-wave symmetries of the gap corresponding to the low hole-doping and heavily hole overdoped cases, respectively.