The parallel propagating transverse modes in a plasma are known to be exact solutions of the MHD and multifluid equations. Here we investigate these waves in a multicomponent plasma consisting of two ion-like species, which are allowed to be fully mobile. In this paper we perturb these exact solutions and investigate modulational or decay instabilities where the pump wave is modified by the daughter waves in regions of instability. In a warm plasma, the parallel modes can interact with transverse and acoustic modes. A tenth-degree polynomial dispersion equation is obtained, describing the interaction of the pump with two acoustic modes and sideband-beat-waves. In the low-temperature regime the effect of a second ion species is to reduce the usual modulational instability, and a new decay instability arises. In the high-temperature regime, two new decay instabilities, narrow in wave number, are found. All of these instabilities involve the additional modes associated with the introduction of a second heavy species.