Hyperdimensional NMR describes the multiple interactions between a large number, N, of coupled nuclear spins. We show how to construct a hypothetical N-dimensional spectrum from a limited set of low-dimensional measurements, exploiting the concept of projection-reconstruction. In the process, many correlation spectra are obtained that were not investigated directly. As an illustration, the hypothetical ten-dimensional spectrum of a small protein (agitoxin) has been reconstructed, and a large number of pairwise correlation spectra have been recorded.