The time shifted pilots (TSP) is a well-known countermeasure against the pilot contamination problem in the massive multiple input and multiple output (MIMO) systems. Recently, two performance enhancement schemes evolved from TSP were developed on top of the single- and two-ring cell structures. In this letter, we aim to answer the puzzle of how to decide the number of rings [denoted by (r_max)] and arrange the time slots for pilot, downlink and uplink transmissions [denoted by the triple (F, D, U)] on top of the multi-ring (MR) cell structures. To this end, we develop a general MR-TSP scheme by dividing a cell into multiple rings and allocating non-overlapped time-slots to different rings for transmitting pilots. Moreover, similar to the conventional TSP scheme, the same time slots can still be shared with cells belonging to different groups. Based on the findings from the numerical results, we develop a principle for deciding r_max and (F, D, U) to meet various system configurations.