The simultaneous collection of multiple spectra using tandem (MS/MS) and multidimensional (MS/MS/MS) mass spectrometry from multiple precursors is demonstrated to yield correspondingly enhanced sensitivity. This approach utilizes Hadamard transform deconvolution and takes advantage of the multichannel dissociation capability of Fourier-transform mass spectrometry. By application of this to an 11-component mixture, the 11 spectra of the products of dissociating 11 different combinations of six of the component molecular ions are measured; Hadamard transformation yields individual spectra of the precursor ions exhibiting a signal-to-noise improvement of 1.8x over spectra measured separately, as predicted by theory. Precursor ion selection with high specificity and product formation with high abundance reproducibility are critical; spurious peaks resulting from imperfect reproducibility can be minimized by using simultaneous equation coefficients reflecting the degree of precursor dissociation. Extension of this technique to MSn spectra is demonstrated with simultaneous MS/MS/MS monitoring of three precursors and three daughters yielding nine spectra representing the nine possible dissociation pathways. For MSn spectra, coding the product relationships for each additional step (e.g., precursor----daughter, daughter----granddaughter) requires elimination of half of the remaining ions. No ions are lost for coding in an improved Hadamard approach in which the combined daughter spectrum of the selected half of the precursors is subtracted from that of the other half.