Refinement is a critical step in supply-driven conceptual design of multidimensional cubes because it can hardly be automated. In fact, it includes steps such as the labeling of attributes as descriptive and the removal of uninteresting attributes, thus relying on the end-users' requirements on the one hand, and on the semantics of measures, dimensions, and attributes on the other. As a consequence, it is normally carried out manually by designers in close collaboration with end-users. The goal of this work is to check whether LLMs can act as facilitators for the refinement task, so as to let it be carried out entirely -- or mostly -- by end-users. The Dimensional Fact Model is the target formalism for our study; as a representative LLM, we use ChatGPT's model GPT-4o. To achieve our goal, we formulate three research questions aimed at (i) understanding the basic competences of ChatGPT in multidimensional modeling; (ii) understanding the basic competences of ChatGPT in refinement; and (iii) investigating if the latter can be improved via prompt engineering. The results of our experiments show that, indeed, a careful prompt engineering can significantly improve the accuracy of refinement, and that the residual errors can quickly be fixed via one additional prompt. However, we conclude that, at present, some involvement of designers in refinement is still necessary to ensure the validity of the refined schemata.