We present an analysis showing which types of systems are most sensitive to electron impact multiple ionization (EIMI). EIMI is the process in which a single electron-ion collision causes two or more electrons to be ejected from the target ion. Most models of collisionally ionized plasmas ignore EIMI. However, EIMI may be important when either (a) there is a rapid change in the electron temperature or (b) the electron energy distribution is non-thermal so that there is a population of electrons with energies larger than the EIMI threshold. As EIMI is difficult to model, most data must come from experiments. As such, we seek to identify and prioritize measurements of systems that are most sensitive to EIMI. For our analysis, we focus on double ionization and compare the timescale for sequential single ionizations from charge state q to q+2 to the timescale for one double-ionization. These timescales are computed from the relevant ionization rate coefficients as a function of temperature and the κ parameter for non-thermal electron energy distributions.