Systematic pressure-dependence studies have been performed on $M{\mathrm{C}}_{8}$ and $M{\mathrm{C}}_{12n}$ ($M=\mathrm{R}\mathrm{b},\phantom{\rule{0ex}{0ex}}\mathrm{C}\mathrm{s}$ and $n=2, 3, 4$) graphite intercalation compounds. Pressure-induced staging phase transitions similar to that which had been previously reported for K${\mathrm{C}}_{24}$ by Clarke et al. were found in these high-stage graphite intercalation compounds ($n\ensuremath{\ge}2$). The $\stackrel{\ensuremath{\rightarrow}}{q}\ensuremath{\perp}c$ x-ray experiments revealed the formation of a 2\ifmmode\times\else\texttimes\fi{}2 superlattice under hydrostatic pressure from the disordered intercalant layers at ambient conditions. The Raman spectra from $\mathrm{Rb}{\mathrm{C}}_{12n}$ ($n=2, 3, 4$) gave clear evidence for the pressure-induced staging transition by showing a change in the Raman intensities of the bounding (1605 ${\mathrm{cm}}^{\ensuremath{-}1}$) and interior (1582 ${\mathrm{cm}}^{\ensuremath{-}1}$) ${E}_{2g}$-like phonon peaks with pressure. In addition, the compressibilities ${k}_{d}$ of Cs${\mathrm{C}}_{8}$ and Rb${\mathrm{C}}_{8}$ were measured as (1.56\ifmmode\pm\else\textpm\fi{}0.05) and (2.42\ifmmode\pm\else\textpm\fi{}0.12)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{2}$/dyn, respectively. The compressibility results indicate that the interlayer-coupling strength varies drastically among alkali-graphite intercalation compounds. The pressure-dependent Raman spectra of Rb${\mathrm{C}}_{8}$ showed an appreciable change in the Fano resonance shape at \ensuremath{\sim} 580 ${\mathrm{cm}}^{\ensuremath{-}1}$ with pressure. The mode-Gr\uneisen constant ${\ensuremath{\gamma}}_{0\ensuremath{\perp}}$ of pristine graphite for the for the interlayer mode ${E}_{2g}$ was found to be 1.66\ifmmode\pm\else\textpm\fi{}0.13. The rates of Raman frequency shifts with respect to pressure, $\frac{\ensuremath{\partial}{\ensuremath{\omega}}_{0}}{\ensuremath{\partial}P}$, were measured to be (0.70\ifmmode\pm\else\textpm\fi{}0.12), (0.51\ifmmode\pm\else\textpm\fi{}0.09), (0.44\ifmmode\pm\else\textpm\fi{}0.05), (0.54\ifmmode\pm\else\textpm\fi{}0.08) ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{kbar}}^{\ensuremath{-}1}$ for the bounding modes of Cs${\mathrm{C}}_{24}$ and $\mathrm{Rb}{\mathrm{C}}_{12n}$ ($n=2, 3, 4$), and (0.78\ifmmode\pm\else\textpm\fi{}0.08), (0.32\ifmmode\pm\else\textpm\fi{}0.12) ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{kbar}}^{\ensuremath{-}1}$ for the interior modes of $\mathrm{Rb}{\mathrm{C}}_{12n}$ ($n=3, 4$), respectively.