Magnetization reversal phenomena (MRP) along magnetic order-order transitions have recently been reported on impurity-doped magnetic systems. Because imperfect long-range magnetic order exists in these systems, it is expected that a systematic investigation of MRP will give physical information on thermomagnetic processes of magnetic systems in the range from the micro- to nanoscales. As a typical order-order transition (a state doubly modulated by helical and canting orders to a collinear ferrimagnetic state) has been known to occur on Cr5S6 at a transition temperature Tt, we investigate the magnetizations of (Cr0.70Ti0.30)5S6 on heating and cooling runs in various magnetic fields. At 20Oe, the field-cooled magnetization just below the Curie temperature has a positive sign; the sign turns negative below the compensation temperature TCM (first step) and finally returns to positive below Tt (second step). The first-step MRP observed in this system is explained by the potential barriers resulting from anisotropy energy when the preferred direction of collinear ferrimagnetic moment reverses. The proposed mechanism for second-step MRP is the pinning effect caused by the impurity atoms (Ti) in the helical long-range-order chains. Comparing other examples of MRPs, we discuss the roles of local impurity centers in the thermomagnetic process in magnetic order-order transitions.