Indefinites are known to give rise to different scopal (specific vs. non-specific) and epistemic (known vs. unknown) uses. Farkas and Brasoveanu (Wiley Blackwell Compan. Semant. 1–26, 2020) explain these specificity distinctions in terms of stability vs. variability in value assignments of the variable introduced by the indefinite. Typological research (Haspelmath in Indefinite pronouns. Oxford University Press, 1997) shows that indefinites have different functional distributions with respect to these uses. In this work, we present a formal framework where Farkas and Brasoveanu (Wiley Blackwell Compan. Semant. 1–26, 2020’s) ideas are rigorously formalized. We develop a two-sorted team semantics that integrates both scope and epistemic effects. We apply the framework to explain the typological variety of indefinites, showing that only lexicalized indefinites have convex meanings in our system (Gärdenfors in The geometry of meaning: semantics based on conceptual spaces. MIT Press, 2014; Steinert-Threlkeld et al. Semant. Pragmat. 16:1-EA, 2023). We account for the restricted distribution and licensing conditions of different indefinites, and we focus on a particular class of indefinites, called epistemic indefinites (Alonso-Ovalle and Menéndez-Benito in Epistemic indefinites: exploring modality beyond the verbal domain. Oxford University Press, 2015).