 This paper studies a three-dimensional Lorentz-like system with higher-order nonlinear terms added to the original Lorentz system. The system exhibits various interesting dynamics such as generic and degenerate pitchfork bifurcations, hopf bifurcations, hidden Lorentz-like attractors, and singularly degenerate heteroclinic cycles with nearby chaotic attractors. Furthermore, it is shown that the parabolic type equilibria are globally exponentially asymptotically stable, and a pair of symmetrical heteroclinic orbits with respect to the z-axis exist. These results provide new insights into the dynamics of the Lorentz-like system family. This article was authored by Heijun Wang, Guiyouku, John Pan, and others.