The structures of biological molecules may soon be determined with X-ray free-electron lasers without crystallization by recording the coherent diffraction patterns of many identical copies of a molecule. Most analysis methods require a measurement of each molecule individually. However, current injection methods deliver particles to the X-ray beam stochastically and the maximum yield of single particle measurements is 37% at optimal concentration. The remaining 63% of pulses intercept no particles or multiple particles. We demonstrate that in the latter case single particle diffraction patterns can be extracted provided the particles are sufficiently separated. The technique has the potential to greatly increase the amount of data available for three-dimensional imaging of identical particles with X-ray lasers.