To help the design of relay protection in power distribution systems, the conditions to guarantee multi-stage three section type overcurrent protection (MTSOP) is deduced. An improved method of coordination by setting the threshold values of current for the cases of three-phase and two-phase short circuit, respectively, is put forward. A looped distribution network is used as an example to discuss the design considerations of MTSOP for interconnected distribution grids. Combined with the coordination by time-delays, four typical modes of multi-stage over-current protection are proposed. The features and setting methods are detailed, respectively. An example is given to demostrate the proposed approach showing that the improved method with different setting values can effectively increase the range of protection. It is also shown that the proposed multi-stage protection modes, design and setting methods are feasible.