There is a theorem of Schwede and Shipley which classifies categories of modules over an A<sub>∞</sub> ring spectrum as those stable presentable (∞,1)-categories with a compact generator. Suppose I allow my A<sub>∞</sub> rings to "have many objects", that is, I consider categories of the form Fun<sub>Sp</sub>(I<sup>op</sup>, Sp) where Sp is the category of spectra, I is a small Sp-enriched category (in some appropriate sense) and Fun<sub>sp</sub> denotes the category of Sp-enriched functors. Is there a classification of which stable presentable categories can be obtained in this way? Is it possible that *all* stable presentable categories are of this form?