Finite amplitude Alfvén-cyclotron waves are believed to play an important role in coronal heating and nonthermal properties of velocity distribution functions. These effects are thought to be due to parametrically unstable Alfvén-cyclotron waves and electrostatic bursts of ion-acoustic like waves. It is shown here that large amplitude Alfvéncyclotron waves propagating in multi-ion plasmas with relative drift velocities between the ion-species, can lead to a new type of nonlinear electrostatic ion-acoustic like instabilities. These instabilities occur when the phase velocity of a forward propagating ion-acoustic wave supported by one ion species become equal to the phase velocity of a backward propagating ion-acoustic wave supported by another ion species. This phenomenon is only possible when relative to the background plasma there are at least two streaming ion components.