The introduction of medical linear accelerators (linacs) capable of producing three different x-ray energies has complicated the process of designing shielding for these units. The conventional approach for the previous generation of dual-energy linacs relied on the addition of some amount of supplementary shielding to that calculated for the higher-energy beam, where the amount of that supplement followed the historical "two-source" rule, also known as the "add one HVL rule," a practice derived from other two-source shielding considerations. The author describes an iterative approach that calculates shielding requirements accurately for any number of multiple beam energies assuming the workload at each energy can be specified at the outset. This method is particularly useful when considering the requirements for possible modifications to an existing vault when new equipment is to be installed as a replacement for a previous unit.