We have measured the magnetoresistance of a two-dimensional electron gas (2DEG) under continuous microwave irradiation as a function of electron density and mobility tuned with a metallic top-gate. In the entire range of density and mobility we have investigated, we observe microwave induced oscillations of large amplitude that are B-periodic. These B-periodic oscillations are reminiscent of the ones reported by Kukushkin [Phys. Rev. Lett. 92, 236803 (2004)] and which were attributed to the presence of edge-magneto-plasmons. We have found that the B-periodicity does not increase linearly with the density in our sample but shows a plateau in the range (2.4-3)x10(11) cm(-2). In this regime, the phase of the B-periodic oscillations is found to shift continuously by two periods.