This paper examines the particle -daa found in the Siberian Turkic language Tuvan. Among its functions, it can mark additive 'also' or mirative 'even' focus, as well as forming polarity sensitive indefinites with a host interrogative pronoun. Depending on the polarity and modality of the sentence, a WH-daa indefinite can be interpreted as a negative polarity item (in the scope of negation), as an any-like universal free-choice item (in the scope of a modal), and as a universal generalized quantifer (in non-modal episodic affirmative sentences). It is argued that all of these roles can be captured by a single semantic contribution from the particle: -daa is a pre-exhaustification operator which activates the subdomain alternatives of its prejacent, and denies them. The difference in interpretation is the result of the nature of the host's subdomain alternatives, and the logical properties of the environment that the host+particle construction appears within.