X-ray reflection spectroscopy is a powerful tool to probe the strong gravity region around black holes, but the available relativistic reflection models have a number of simplifications that lead to systematic uncertainties (not fully under control) in the measurement of the properties of a source. In Paper I, we considered the case of an optically thin plunging region and we studied the impact of the radiation produced by the other side of the disk or circling the black hole one or more times. In the present paper, we discuss the case of an optically thick plunging region and we study the impact of the reflection spectrum of the plunging gas. We show that the contribution of such radiation is more important for low values of the black hole spin parameter and large values of the viewing angle, and it decreases significantly as the spin parameter increases and the inclination angle decreases. While the estimate of some parameters may be affected by the reflection spectrum of the plunging gas if this is not included in the theoretical model, we find that such radiation does not appreciably limit our capability of testing the Kerr black hole hypothesis.