On the one hand, it is often assumed that the Rubber Hand Illusion (RHI) is constrained by a structural body model so that one cannot implement supernumerary limbs. On the other hand, several recent studies reported illusory duplication of the right hand in subjects exposed to two adjacent rubber hands. The present study tested whether spatial constraints may affect the possibility of inducing the sense of ownership to two rubber hands located side by side to the left of the subject's hand. We found that only the closest rubber hand appeared both objectively (proprioceptive drift) and subjectively (ownership rating) embodied. Crucially, synchronous touch of a second, but farther, rubber hand disrupted the objective measure of the RHI, but not the subjective one. We concluded that, in order to elicit a genuine RHI for multiple rubber hands, the two rubber hands must be at the same distance from the subject's hand/body.