With the advancement of optical communication, optical encoding, and optical storage technologies, the demand for tunable mode-locked fiber lasers (MLFL) with soliton molecules is continuously increasing. The novel ternary two-dimensional topological insulator PbBi4Te7 provides an effective pathway for realizing tunable soliton molecules in MLFL. This study employs a combined liquid phase exfoliation (LPE) and optical deposition methods (ODMs) to prepare PbBi4Te7 saturable absorbers (SAs). In the same MLFL, conventional soliton (CS), controllable soliton molecules with adjustable soliton numbers and intervals, as well as multi-soliton complexes are obtained. Among them, a fundamental frequency CS pulse at 22.778 MHz with a signal-to-noise ratio (SNR) of up to 71 dB is achieved. By adjusting the pump power, 2nd-, 3rd-, 4th-, 9th-, and 11th-order soliton molecules were obtained. By tuning the polarization controller (PC), switching of the soliton interval for 2nd-, 3rd-, and 4th-order soliton molecules was achieved. Additionally, we obtained three unequally spaced multi-soliton complexes: 2 + 1 soliton molecule, 2 + 2 soliton molecule complex and 2 + 2 + 1 soliton molecule complex. The results indicate that PbBi4Te7-SA exhibits outstanding nonlinear optical performance.