We report the observation of the interaction of bound multiple solitons generated by orthogonally polarized, highamplitude pulses in strongly birefringent fibers. For the birefringence used, the threshold amplitude for the interaction is higher than that of the onset of second-order solitons on each axis. The characteristics of the output pulses are in good agreement with the results of a numerical simulation of this interaction. A general investigation of this effect is carried out at high values of birefringence, and it is found numerically that, even though the system is nonintegrable, the description of its evolution appears to be reduceable to a finite number of effective degrees of freedom.