Grammatical theories which specify grammars by means of symbolic well-formedness constraints (e.g., Context Free Grammars, HPSG, LFG, Minimalism, Dependency Grammars, etc.) are ill-suited to model the (semantically and statistically) gradual character of grammatical change as it manifests in successive historical corpora. Grammatical theories which claim that the language system is subject to change based on what speakers do in life (i.e., usage-based accounts) are better-suited to handle such phenomena. Nevertheless, current usage-based theories (e.g., Cognitive Grammar, Construction Grammar) lack a clearly formalized model that specifies how usage can affect the grammatical system. In this paper, we describe Stretched Tree Metric Grammars (STMGs), a new formal model of syntax and semantics that exhibits usage-based effects. We show that the model can generate and parse simple sentences. Then we show how it supports morphological innovation in appropriately limited circumstances. We conclude by noting that STMGs are closely related to Large Language Models (LLMs), but they have the benefit of being more analytically interpretable.