A theoretical model for the free expansion of a plasma with three and multiple electron temperatures is developed. The three and multiple peak structures exhibited in ion velocity distributions, which have often been observed experimentally, have been reproduced by the self similar solutions successfully. It is shown that the number of the peaks for ion spectra are closely connected with mumber of electron components including in plasma. The depth of the dip between two adjacent peaks is particularly sensitive to the adjacent electron temperature ratio, the position of the dip depends on corresponding electron number density ratio, they are also affected by coupling of the other electron components. The regions in the parameter space where the self similar solutions are available are discussed.