For the evaluation of interaction design, usually prototypes are created. For creating high-fidelity prototypes, automated generation may be an option, at least in the case of graphical (Web) user interfaces (GUIs). However, the usability of fully-automatically generated GUIs is considered unsatisfactory. In our opinion, a major reason is that most previous approaches to automated GUI generation do not sufficiently explore alternatives in the design space of GUIs, in particular not automatically. Can existing techniques for automated Web GUI generation from high-level representations of interaction design comprehensively support the exploration of design alternatives? We explain and address this problem and research question, and investigate exploring alternatives (at different stages), both by the designer and the generator tool, which receives high-level representations of interaction design as its input. For the designer, exploring alternatives involves providing alternative high-level models and transformations, selecting from Web GUI interaction strategies (e.g., scrolling vs. using tabs) and defining customizations. Exploring alternatives means for the AI-based generator tool creating alternative widgets and layouts in the course of a heuristic search, and tailoring for different target devices, according to the Web GUI interaction strategy selected by the designer. For making automated GUI generation applicable in the context of general interaction design, we also propose a new iterative and incremental interaction design process centered around automated generation.