The tidally induced fragmentation of a rotating protostellar cloud has been modelled using a 3-D hydrodynamic code. The tidal pattern includes the effects of p = 3 nearby sources not aligned with the equatorial plane of the cloud, consistent with a realistic model for protostellar collapse. Clouds with alpha = 0.25 experience binary fragmentation through a sequence of intermediate forms: ring --> deformed ring --> bar, with increasing size of the tidal perturbation delta. Lower alpha(= 0.10 and 0.05) clouds undergo intermediate m = 2 bar fragmentation. For delta < approximately 1.60, the bar m = 2 mode is distorted by differential rotation into a ring-like structure which breaks up into a number (> 2) of small-length fragments. This phase is followed by a rapid coalescence of the fragments leading to the formation of either a binary or a triple system. For delta > 1.60, the bar mode resists rotational distortion inhibiting intermediate multiple fragmentation. Only for delta > approximately 5.0, tidal forces may disrupt the collapse preventing fragmentation. A comparison with delta = 0 models shows that tidal perturbations of moderate size (delta < approximately 5.0) accelerate fragmentation and enrich the structure of collapse.