  We study the nontrivial interplay of the well known \emph{pairing} and the
more complex \emph{quarteting} correlations in the particular case of $N>Z$
atomic nuclei. Within the new Analytical Disentangled Condensate model, by
implementing the notion of \emph{fractional degeneracy} we obtain the clear
physical picture of a rather weakly interacting mixture of quartet and neutron
pair condensates which mainly feel each other's influence through Pauli
blocking. The basic idea of our approach may be generalized in order to
scrutinize the extent to which similar manifestations are present in various
many-body systems.
