We describe new developments aimed to extend the capabilities and the sensitivity of the (e,2e)(e,3e) multicoincidence spectrometer at Orsay University [Duguet et al., Rev. Sci. Instrum. 69, 3524 (1998)]. The spectrometer has been improved by the addition of a third multiangle detection channel for the fast "scattered" electron. The present system is unique in that it is the only system which combines three toroidal analyzers all equipped with position sensitive detectors, thus allowing the triple coincidence detection of the three electrons present in the final state of an electron impact double ionization process. The setup allows measurement of the angular and energy distributions of the ejected electrons over almost the totality of the collision plane as well as that of the scattered electron over a large range of scattering angles in the forward direction. The resulting gain in sensitivity ( approximately 25) has rendered feasible a whole class of experiments which could not be otherwise envisaged. The setup is described with a special emphasis on the new toroidal analyzer, data acquisition hardware, and data analysis procedures. The performances are illustrated by selected results of (e,2e) and (e,3e) experiments on the rare gases.