For the first time, we demonstrate the possibility to switch between three distinct pulse regimes in a dissipative dispersion-managed (DM) fibre laser by solely controlling the gain saturation energy. Nonlinear Schrödinger equation based simulations show the transitions between hyper-Gaussian similaritons, parabolic similaritons, and dissipative solitons in the same laser cavity. It is also shown that such transitions exist in a wide dispersion range from all-normal to slightly net-normal dispersion. This work demonstrates that besides dispersion and filter managements gain saturation energy can be a new degree of freedom to manage pulse regimes in DM fibre lasers, which offers flexibility in designing ultrafast fibre lasers. Also, the result indicates that in contrast to conservative soliton lasers whose intensity profiles are unique, dissipative DM lasers show diversity in pulse shapes. The findings not only give a better understanding of pulse shaping mechanisms in mode-locked lasers, but also provide insight into dissipative systems.