This paper extends the empirical coverage of the Autosegmental Input Strictly Local (A-ISL) framework (Chandlee and Jardine, 2019) by analyzing three tonal processes: floating tone suffixation in Cantonese, metrical dominance effect in Shanghai Chinese, and a combination of floating tones and metrical dominance in Suzhou Chinese. I show both the adequacy and inadequacy of the current A-ISL framework: it locally resolves some tonal processes that are otherwise non-local (Shanghai), but fails to account for other empirical data due to a lack of tonal membership specification (Suzhou). With the addition of a morphological affiliation tier, I propose an analysis for the Suzhou data. The paper contributes to our typological knowledge of computational locality and autosegmental phonological representations
