The Extended interaction amplifier (EIA) has been extensively studied and applied for its numerous advantages. Here, an extended interlaced staggered resonant cavity (EISRC) is proposed based on the staggered dual-vane slow wave structure. Then a traveling - standing - traveling wave circuit is constructed, where a section of slow wave structure is employed for inputting the signal, two resonant cavities to modulate the signal, followed by a section of slow wave structure to output the signal. The voltage is 19.6 kV for the frequency of 94 GHz. By using CST Eigenmode Solver, the M2R/Q of 2π mode and 13/7π mode of the 7-period cavities have been explored, which are 22.45 for the 13/7π mode and 4.31 for the 2π mode. Subsequently, the 13/7π mode is chosen as the working mode. According to the bunching theory of the klystron, when the frequency of the resonant cavity is higher than the operating frequency, the resonant cavity gap presents inductive impedance, which is conducive to the clustering of the electron beam, and the optimal tuning of the end-front cavity can significantly improve the efficiency of the klystron. Parametric tuning is used to stagger the frequencies of the cavities to obtain a wider and flatter gain-frequency curve. When the resonant frequencies of the two resonant cavities increase sequentially, the gain notch of the output signal gradually disappears, effectively expanding the operating bandwidth of the entire circuit. The final design solution has a frequency of 94.25 GHz for resonant cavity 1 and 94.35 GHz for resonant cavity 2. The operating current is 0.3 A and the input port is fed with a 10 mW sinusoidal electromagnetic wave signal. The particle-in-cell (PIC) simulation result shows that the saturated output power of the EISRC is 242.52 W at 94.04 GHz, corresponding gain of 40.89 dB. The 3 dB bandwidth is 220 MHz, comparing the previous design with a 3 dB bandwidth of 60 MHz [1], a significant increase in bandwidth was achieved.