The kinematic and pitch angle scattering constraints for multiple shock encounters to occur are investigated. The results suggest that (1) large particle anisotropies and a large number or shock encounters are not mutually exclusive and (2) solar wind ions are not directly injected into the nearly perpendicular interplanetary shock acceleration process. Also, the average number of shock encounters required to accelerate an ion between two energies is calculated. The results are consistent with the shock geometry dependence observed in interplanetary shock spike and corotating interaction region associated energetic ion events.