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Phase separation of biomolecules could be mediated by both specific and non-specific interactions. How the interplay between non-specific and specific interactions along with polymer entropy influences phase separation is an open question. We address this question by simulating self-associating molecules as polymer chains with a short core stretch that forms the specifically interacting functional interface and longer non-core regions that participate in non-specific/promiscuous interactions. Our results show that the interplay of specific (strength, ϵsp) and non-specific interactions (strength, ϵns) could result in phase separation of polymers and its transition to solid-like aggregates (mature state). In the absence of ϵns, the polymer chains do not dwell long enough in the vicinity of each other to undergo phase separation and transition into a mature state. On the other hand, in the limit of strong ϵns, the assemblies cannot transition into the mature state and form a non-specific assembly, suggesting an optimal range of interactions favoring mature multimers. In the scenario where only a fraction (Nfrac) of the non-core regions participate in attractive interactions, we find that slight modifications to either ϵns or Nfrac can result in dramatically altered self-assembled states. Using a combination of heterogeneous and homogeneous mix of polymers, we establish how this interplay between interaction energies dictates the propensity of biomolecules to find the correct binding partner at dilute concentrations in crowded environments. Author summary: Biological function relies on the ability of biomolecules to bind to specific interaction partners. In the crowded cellular milieu, the process of biomolecules binding to specific interaction partners to carry out a function is non-trivial. A mere diffusion-limited meeting of interaction partners in space does not ensure biomolecular function. Rather, even when in contact, these molecules have to find the correct orientations to carry out their function. Further, for dynamic biomolecules such as polymers, the functional configuration is often one of several possible configurations. In this scenario, assuming the functional configuration after binding involves overcoming a significant entropic barrier. Therefore, the interacting biomolecules have to dwell in contact long enough before they reorganize to find the functional orientation! While functional contacts offer an enthalpic gain, they are often only a small fraction of all protein-protein interactions. Therefore, in this paper, we study the role played by non-functional, promiscuous interactions in shaping the thermodynamics and kinetics of the formation of specific interactions. Our results suggest that there exists an optimal range of non-specific interaction strengths, which promotes the process of biomolecular complexes finding the functional configurations. [ABSTRACT FROM AUTHOR]