A recent dispute about formalizations of Meinongian object theory, involving dual modes of predication or the distinction between constitutive (nuclear) and extraconstitutive (extranuclear) properties, is reexamined in historical and philosophical perspective. The distinction itself and the choice for object theory theorization that it motivates is intrinsically interesting, and suggests a fruitful branching set of alternatives for logic and philosophy to explore. Counterexamples to a previous attempt to reduce dual modes to univocal predication under the constitutive-extraconstitutive property distinction are met by an amended reduction, supporting the conclusion that constitutive-extraconstitutive properties are conceptually more basic than dual modes of predication, and a generalized argument to show that no reduction or intertranslation from one distinction idiom to the other can succeed is refuted, in the general context of developing the foundations for Meinongian logic and theory of meaning.