Some languages around the Pacific have multiple possessive classes of alienable constructions using appositive nouns or classifiers. This pattern differs from the most common kind of alienable/inalienable distinction, which involves marking, usually affixal, on the possessum, and has only one class of alienables. The Japanese language isolate Ainu has possessive marking that is reminiscent of the Circum-Pacific pattern. It is distinctive, however, in that the possessor is coded not as a dependent in an NP but as an argument in a finite clause, and the appositive word is a verb. This paper gives a first comprehensive, typologically grounded description of Ainu possession and reconstructs the pattern that must have been standard when Ainu was still the daily language of a large speech community; Ainu then had multiple alienable class constructions. We report a cross-linguistic survey expanding previous coverage of the appositive type and show how Ainu fits in. We split alienable/inalienable into two different phenomena: Argument structure (with types based on possessibility: optionally possessible, obligatorily possessed, and non-possessible) and valence (alienable, inalienable classes). Valence-changing operations are derived alienability and derived inalienability. Our survey classifies the possessive systems of languages in these terms.