Bifurcations from non-trivial linear fundamental paths are investigated in a class of static elastic systems admitting large precritical deformations, in which axial softness plays a central role in shaping the stability landscape. A distinctive feature of these systems is the occurrence of multiple, sequential losses and recoveries of stability along the fundamental path, here referred to as a cascade of destabilizations and restabilizations, a phenomenon which triggered considerable interest in the recent literature on elastic structures, where even two such events along the fundamental path have been regarded as remarkable. The analysis reveals the occurrence of the phenomenon when the underlying inextensible structure possesses buckling modes of different shape, whose critical loads exchange order as a slenderness parameter varies, as in compressed plates and beams on elastic foundation. Illustrative discrete systems are examined in detail, acting as transparent prototypes that highlight the mechanisms through which eigenvalue merging and axial compliance cooperate to produce this rich bifurcation structure. Results are extended to a continuous model of beam.
