  By varying a general pair condensate (VPC), we explore the multiplet of
minima in even-even nuclei from $sd$ shell to media-heavy $sdg7h11$ shell,
which may provide the foundation of universal coexistence. The VPC calculation
is limited within a single major shell, and thus the conventional
interpretation for the coexistence near magic number, i.e.,
multiple-particle-hole excitation across a major shell gap, does not account
for coexistence observed in this work. The inclusion of all possible pairing
channel is crucial to this ``new'' type of shape coexistence, or increase the
energy minima of such coexistence. The angular-momentum projected VPC (PVPC) is
adopted to further calculate the low-lying level scheme of some light nuclei,
and to identify the band structures emerging from the coexistence. Well
agreement between the PVPC results and the experimental data is achieved, and
thus the picture of universal coexistence is experimentally supported, at
least, in light nuclei.
