In Part I [J. Vac. Sci. Technol. A 13, 467 (1995)] of this article pressure versus time was calculated for the evacuation of a vacuum system with a reversibly adsorbed phase at coverages less than one monolayer; in Part II this analysis is extended to the multilayer region, i.e., from the saturated vapor pressure (p(s)) to the pressure corresponding to one monolayer (p(m)) the gas flow is viscous in this range. In this pressure range the ratio of adsorbed to gas phase molecules is small (less than a few percent). As a practical example, the adsorbed phase is taken to be water at about 300 K. A recently proposed empirical adsorption isotherm is used that is a good fit to experiment from p(s) to p(m), unlike existing isotherms that only cover parts of this range. Using this isotherm, the pressure and coverage as a function of time in the pressure range from p(s) to p(m) are calculated. It is shown that, for the reference system chosen (vol 17 l, surface area 4.5 x 10(3) cm(2)), as the system is pumped down, the pressure remains constant for a few seconds at a pressure slightly less than p(s) and then falls to p(m) in essentially the same way as in the absence of an adsorbed phase; this occurs because the number of molecules in the adsorbed phase is much less than in the gas phase. For systems with the pumping parameter S/A<5x10(-3) (S pumping speed, l s(-1), A=area of adsorbing surface, cm(2)) the decrease in temperature caused by the desorption of multilayers of water is too small to have any significant effect on the desorption rate; for systems with higher values of SIA the temperature drop may be significant.