Double plasmons are unique fingerprints of dynamical correlations in the model of a free-electron gas beyond the random phase approximation. A combined experimental and theoretical study of double-plasmon excitations in three simple metals Na, Mg, and Al is presented. The intensities, spectral shapes, and dispersions of these excitations are analyzed as a function of momentum. The measured double-plasmon intensity is found to increase with the decreasing electron density, which is in good agreement with the expectations of strength of the correlation effects as a function of the electron gas density. The overall quantitative agreement between the experimental and the theoretical results is very good, while the remaining discrepancies may be due to higher order correlation effects and band-structure effects.