We provide a principled account of the morphosyntax-semantics interface of non-root modals in two Romance languages (Spanish/French) vs. English. While English modals are morphologically impoverished, Romance modals are fully inflected for tense and aspect and the possible combinations of tense and aspect constrain the range of construals available: epistemic vs. metaphysical. We uniformly derive the range of possible construals from a restricted set of assumptions: (i) Tense/t°, Modal/m°, Aspect/asp° and v° each contribute to the temporal calculus of the clause in which they occur a time argument projected in the syntax as a Zeit-P; (ii) zeit-ps can enter into anaphoric and scopal dependencies. This proposal derives the temporal construals of non-root modals from a single phrase-structure (Tense-P > Modal-P > Aspect-P) without appealing to dedicated hierarchies of functional projections. Syntactic movement of time arguments (Zeit-Ps) and/or temporal heads (t°/asp°) ultimately accounts for cross-linguistic variation in the morphosyntax of these construals.