Dynamic processes such as chemical exchange or rotations between inequivalent orientations can affect the magic-angle spinning (MAS) and the multiple-quantum (MQ) MAS NMR spectra of half-integer quadrupolar nuclei. The present paper discusses such dynamic multisite MAS and MQMAS effects and applies them to study the dynamic processes that occur in the double perovskite cryolite, Na3AlF6. Dynamic line shape simulations invoking a second-order broadening of the central transition and relying on the semiclassical Bloch-McConnell formalism for chemical exchange were performed for a variety of exchange models possessing different symmetries. Fitting experimental variable-temperature cryolite 23Na NMR data with this formalism revealed that the two inequivalent sodium sites in this mineral undergo an exchange characterized by a broad distribution of rates. To further assess this dynamic process a variety of 27Al and 19F MAS NMR studies were also undertaken; quantitative 27Al-19F dipolar coupling measurements then revealed a dynamic motion of the AlF6 octahedra that were qualitatively consistent with predictions stemming from molecular dynamic simulations on this double perovskite.