  Characterizing multipartite quantum correlations beyond two parties is of
utmost importance for building cutting edge quantum technologies, although the
comprehensive picture is still missing. Here we investigate quantum
correlations (QCs) present in a multipartite system by exploring connections
between monogamy score (MS), localizable quantum correlations (LQC), and
genuine multipartite entanglement (GME) content of the state. We find that the
frequency distribution of GME for Dicke states with higher excitations
resembles that of random states. We show that there is a critical value of GME
beyond which all states become monogamous and it is investigated by considering
different powers of MS which provide various layers of monogamy relations.
Interestingly, such a relation between LQC and MS as well as GME does not hold.
States having a very low GME (low monogamy score, both positive and negative)
can localize a high amount of QCs in two parties. We also provide an upper
bound to the sum of bipartite QC measures including LQC for random states and
establish a gap between the actual upper bound and the algebraic maximum.
