The iterative pulsation theory is used to extend the pulsational work integral (long used in the study of pulsating stars) to fourth order in the amplitudes for the case of two simultaneously energized modes. It is shown that when the iterative theory is used to evaluate the extended integral, scale factors can be obtained without referring to external data. The procedure leads to a geometric analysis of modal selection, performed in the space spanned by the amplitudes of the two modes. Modal selection categories are obtained, identical to those of Stellingwerf (1975) and Simon et al. (1980). A brief discussion of the double mode phenomenon is presented, viewed from the perspective of an iterative theory of modal selection.