We report the experimental study of the fine structure of bifurcation and hysteresis behaviors under two control parameters in a weakly ionized cylindrical rf magnetoplasma system that supports nonlinear ionization drift waves. With increasing rf power up to the onset of the quasiperiodic state, the system shows a cascade of hysteresis loops with an abrupt change of the collective mode for each subcritical bifurcation. Fine structures such as the embedded small hysteresis loops, which correspond to multistability, and the backward supercritical subharmonic and intermittent bifurcations were observed. The effects of changing pressure, for example, the conversion from subcritical to supercritical bifurcation through a tricritical point, are also presented and discussed.