Previous experimental studies of superradiance (SR) in multi-level systems have been explainable using the predictions of the well-known simple two-level SR model. However our recent study [K. Nakajima et al., J. Phys. Soc. Jpn. 84, 054301 (2015)] using EUV free-electron laser excitation of helium atoms, where SR was observed at wavelengths of 502, 668, and 728 nm, revealed behaviour which necessitates a full multi-level treatment of the SR development. In this paper, we report simulations of the initial excitation by the FEL pulses, and the subsequent development of multi-level SR. The results of the simulation reproduce the experimental findings, and reveal that competitive SR on two transitions with a common upper level plays an important role in the development of the system.