Wave-particle interactions are believed to be one of the most important kinetic processes regulating the heating and acceleration of solar wind plasma. One possible explanation for the observed preferential heating of alpha (He+2) ions relies on a process similar to a second-order Fermi acceleration mechanism. In this model, heavy ions are able to resonate with multiple counter-propagating ion-cyclotron waves, while protons can encounter only single resonances, resulting in the subsequent preferential energization of minor ions. In this work, we address and test this idea by calculating the number of plasma particles that are resonating with ion-cyclotron waves propagating parallel and antiparallel to an ambient magnetic field B-0 in a proton/alpha plasma with cold electrons. Resonances are calculated through the proper kinetic multispecies dispersion relation of Alfven waves. We show that 100% of the alpha population can resonate with counter-propagating waves below a threshold vertical bar Delta U-alpha p/nu(A)vertical bar < U-0 + a(beta(p) + beta(0))(b) in the differential streaming between protons and He+2 ions, where U-0 = -0.532, a = 1.211, beta(0) = 0.0275, and b = 0.348 for isotropic ions. This threshold seems to match with constraints of the observed Delta U-alpha p in the solar wind for low values of the plasma beta (beta(p)). Finally, it is also shown that this process is limited by the growth of plasma kinetic instabilities, a constraint that could explain alpha-to-proton temperature ratio observations in the solar wind at 1 au.