The kinetic properties of the solar wind protons (ions), like their temperature anisotropy and the resulting instabilities, are, in general, investigated considering only the proton core (or thermal) populations. The implication of the suprathermal halo components is minimized or just ignored, despite the fact that their presence in the solar wind is continuously reported by the observations, and their kinetic energy density may be significant. Whether they are originating in the corona or solar wind, the energetic particles may result from acceleration by the plasma turbulence or from the pitch angle scattering of the streaming protons by the self-generated fluctuations. The presence of suprathermal protons in the heliosphere suggests, therefore, a direct implication in resonant interactions, e.g., Landau and cyclotron, with plasma particles. This paper presents the results of a first investigation on the interplay of the proton core and suprathermal halo, when both these two populations may exhibit temperature anisotropies, which destabilize the electromagnetic ion (proton) cyclotron (EMIC) modes. These results clearly show that for conditions typically encountered in the solar wind, the effects of the suprathermals can be more important than those driven by the core. Remarkable are also the cumulative effects of the core and halo components, which change dramatically the instability conditions.