The spatial evolution of multi-peaked microwave magnetic envelope solitons in a thin yttrium iron garnet (YIG) film has been measured and analyzed. The experiments were done on a long and narrow 5-m-thick single-crystal YIG film strip. Double-peaked and triple-peaked magnetostatic backward volume wave soliton pulses were excited at a nominal carrier frequency of 7.0 GHz. The measurements utilized a movable inductive magnetodynamic probe detection system. The formation of these multi-peaked soliton (MPS) pulses is a two step process. First, an initial single large amplitude pulse gradually separates into two or more nonsolitonic peaks. After a certain propagation time, these nonsolitonic peaks evolve, in sequence, into solitonic peaks with constant phase (CP) and an overall stair-like profile. Typically, the larger amplitude peaks lead in time and become solitonic first. As the MPS signals propagate and decay, the peaks lose their CP character in reverse sequence. The region of existence for the "fully formed" MPS pulses for which all the individual peaks have CP character is extremely narrow, typically on the order of a few tenths of a millimeter. The velocities of the individual peaks scale linearly with the peak powers. A nonlinear response analysis of the peak velocity based on the method of envelopes gives a reasonable match to the data.