  We discuss in detail the coupled-channels approach for the large-angle
quasi-elastic scattering in massive systems, where many degrees of freedom may
be involved in the reaction. We especially investigate the effects of single,
double and triple phonon excitations on the quasi-elastic scattering for
$^{48}$Ti,$^{54}$Cr,$^{56}$Fe,$^{64}$Ni and $^{70}$Zn$+^{208}$Pb systems, for
which the experimental cross sections have been measured recently. We show that
the present coupled-channels calculations well account for the overall width of
the experimental barrier distribution for these systems. In particular, it is
shown that the calculations taking into account single quadrupole phonon
excitations in $^{48}$Ti and triple octupole phonon excitations in $^{208}$Pb
reasonably well reproduce the experimental quasi-elastic cross section and
barrier distribution for the $^{48}$Ti$+^{208}$Pb reaction. On the other hand,
$^{54}$Cr,$^{56}$Fe,$^{64}$Ni and $^{70}$Zn$+^{208}$Pb systems seem to require
the double quadrupole phonon excitations in the projectiles in order to
reproduce the experimental data.
