The question of whether differentially marked objects should be linked with Case licensing or some other mechanism in the grammar has given rise to numerous debates. Addressing contexts of differential object marking (DOM) with oblique morphology, this article shows that, while the Case licensing approach might be adequate for varieties of Spanish, oblique differential marking rather signals an independent licensing operation, beyond Case, in languages like Romanian, Gujarati or Mandarin Chinese. This additional mechanism, relevant at the syntax-semantics-pragmatics interface, tracks the role of grammaticalized animates or how the speaker relates to other entities in the discourse. Additionally, the data examined here indicate that objects can come in a variety of sizes and structures, with distinct licensing constraints, such that the divide Case licensed/unlicensed or Case licensing/(pseudo-)incorporation is not enough.