Transient jet flame propagation under newly proposed multistage pre-chambers is studied in a constant-volume combustion chamber with a high-speed schlieren photography system. Various combustion behaviors, including the flame tip velocity, jet emergence timing, projected flame area, pressure, and heat release rate, are investigated under different pre-chamber structures. The present work will provide constructive insight into the design, manufacture, and application of turbulent jet ignition engines. It is shown that the pre-chamber structure determines the main chamber flame development by influencing the flame development inside the pre-chamber. As the flame is accelerated by an obstacle in the pre-chamber, faster exit velocity of hot jet and intense turbulence are observed in the main chamber. In addition, the overall development of the jet flame in the main chamber can be separated into two stages, the former of which is dominated by jet flows, while the latter stage is controlled by the chemical reaction under different excess air coefficients, presenting turbulent combustion characteristics. In this work, six ignition modes under ultra-lean conditions are observed, including (1) jet ignition occurrence on the entire jet surface due to the sufficiently high reactivity; (2) local ignition in the middle of the hot jet; (3) local multipoint ignition and ignition at the jet tip; (4) ignition induced by delayed burning at the jet root; (5) jet tip ignition with backward flame propagation; and (6) global extinction. For the effect of initial pressure, it is found that under stoichiometric conditions, the initial pressure has a minor influence on flame tip propagation, while it significantly influences pressure evolution and heat release rate. However, the increase in initial pressure can improve flame propagation and pressure evolution under lean conditions. Under near-extinction conditions, the ignition mode could be switched from unstable ignition to stable ignition. A numerical simulation is also conducted to reveal the flame development inside the pre-chamber under different pre-chamber structures.