  This paper investigates the excitation of various natural modes in a
magnetized bi-ion or dusty plasma. The excitation is provided by parametrically
pumping the magnetic field. Here two ion-like species are allowed to be fully
mobile. This generalizes our previous work where the second heavy species was
taken to be stationary. Their collection of charge from the background neutral
plasma modifies the dispersion properties of the pump and excited waves. The
introduction of an extra mobile species adds extra modes to both these types of
waves. We firstly investigate the pump wave in detail, in the case where the
background magnetic field is perpendicular to the direction of propagation of
the pump wave. Then we derive the dispersion equation relating the pump to the
excited wave for modes propagating parallel to the background magnetic field.
It is found that there are a total of twelve resonant interactions allowed,
whose various growth rates are calculated and discussed.
