A three mirror Fabry-Perot interferometer system is described in which the laser cavity is made n times the length of the second cavity. This results in an n fold increase in the number of fringes observed provided that at least n axial laser modes are excited. A theoretical analysis of the instrument gives fringe forms similar to those obtained experimentally for an n=5 arrangement. The instrument should be very useful for electron density measurements in transient plasmas where refraction effects prevent interferometry at long wavelengths yet many fringes are required for accuracy of measurement. By noting the sequence of the individual fringes, each of which has a characteristic amplitude, it is possible to identify turnover points in electron density.