The most prominent among the constructions included under the rubric of non-canonical constructions here are the so-called dative subject constructions, where what appears to be a subject is marked by a dative case as in the Latin example, Mihi est liber 'I have a book.' These constructions and their variants involving other cases than dative have been the center of focused attention for more than twenty years among the specialists of South Asian languages, Japanese, Icelandic, Quechua, and others, in which a similar type of construction exists. The past analyses under various theoretical persuasions generally agree that these constructions are transitive with the assumption that the two relevant noun phrases are (direct) arguments of the lexical predicates. In this talk, I attempt to show that these past analyses are mistaken and that these non-canonical constructions are basically intransitive. Specifically, I advance a hypothesis that they are to be analyzed as variants of double-subject constructions (e.g. [Mihi [est liber]]), where only one noun phrase is a lexically selected argument, the other being sanctioned by a clausal predicate. Also explored are the semantico-pragmatic reasons for the elliptical nature of the relevant intransitive predications (e.g. Latin Liber est) and the factors governing the distribution of subject properties over the 'large subject' and the 'small subject' of the double subject construction. Finally, wider descriptive and theoretical implications of the proposed analysis are drawn.