The goal of linguistic science is to understand the nature of the psychological system responsible for our linguistic capacities. The complexity of this system, and of the larger psychological system of which it is a constituent, makes achieving this goal very difficult. In particular, such complexities in the target system result in patterns of observations that do not lend themselves to neat generalizations. One central difficulty in linguistic theory is thus determining just how far our theorizing is allowed to stray from these complex data. I will examine case studies from three branches of linguistic theory: syntax, semantics, and language acquisition. In each case, we will see advocates of opposing stances on this question. One side will argue that our theories ought stick very closely to the observed data, and thus produce complex and particularized theories capable of doing so. The other will argue for more abstract theories, which suggest explanatory depth and unification, but at the cost of apparent empirical adequacy. In all three cases, I shall argue that neither extreme position is appropriate, when understood as excluding the other. I shall instead develop a variety of pluralist strategies, attempting to integrate the two approaches by developing a battery of different representations of target systems which are individually insufficient in various ways, but collectively capable of accounting for the phenomena. The overall aim is to develop a clear understanding, drawn from contemporary work in the philosophy of science, of the methodological foundations of linguistic theory.