LLMs offer unprecedented capabilities for generating code and prose; creating systems that take advantage of these capabilities can be challenging. We propose an artifact-centered iterative disambiguation process for using LLMs to iteratively refine an LLM-based system of subcomponents, each of which is in turn defined and/or implemented by an LLM. A system implementing this process could expand the experience of end-user computing to include user-defined programs capable of nearly any computable activity; here, we propose one approach to explore iterative disambiguation for end-user system design.