Topological photonic systems offer light transport that is robust against defects and disorder, promising a new generation of chip-scale photonic devices and facilitating energy-efficient on-chip information routing and processing. However, present quasi one dimensional (1D) designs, such as the Su–Schrieffer–Heeger and Rice–Mele models, support only a limited number of nontrivial phases due to restrictions on dispersion band engineering. Here, a flexible topological photonic lattice on a silicon photonic platform is experimentally demonstrated that realizes multiple topologically nontrivial dispersion bands. By suitably setting the couplings between the 1D waveguides, different lattices can exhibit the transition between multiple different topological phases and allow the independent realization of the corresponding edge states. Heterodyne measurements clearly reveal the ultrafast transport dynamics of the edge states in different phases at a femtosecond scale, validating the designed topological features. The study equips topological models with enriched edge dynamics and considerably expands the scope to engineer unique topological features into photonic, acoustic, and atomic systems.