Data acquisition using the Carr-Purcell-Meiboom-Gill (CPMG) train of pi pulses has been recently explored in multiple quantum magic angle spinning (MQMAS) nuclear magnetic resonance of half-integer quadrupolar nuclei [T. Vosegaard, F. H. Larsen, H. J. Jakobsen, P. D. Ellis, and N. C. Nielsen, J. Am. Chem. Soc. 119, 9055 (1997)]. Significant increase of sensitivity can be obtained by using this technique at the expense of spectral definition, as the spectrum transforms into a manifold of narrow sidebands. A detailed analysis of the CPMG method, with emphasis on the MQMAS experiment, is presented. The MQ-QCPMG-MAS approach is adapted to spin-5/2 nuclei. Several numerical methods of data treatment are shown that allow for improvement of the definition of the sideband envelope, reconstruction of the standard line shape, and improvement of S/N ratio via optimized filtering. Theoretical and experimental estimates of signal enhancement through proper acquisition and processing of MQ-QCPMG-MAS data are given.