Broad exploration of references is critical in the visual design process. While text-to-image (T2I) models offer efficiency and customization of exploration, they often limit support for divergence in exploration. We conducted a formative study (N=6) to investigate the limitations of current interaction with the T2I model for broad exploration and found that designers struggle to articulate exploratory intentions and manage iterative, non-linear workflows. To address these challenges, we developed Expandora. Users can specify their exploratory intentions and desired diversity levels through structured input, and using an LLM-based pipeline, Expandora generates tailored prompt variations. The results are displayed in a mindmap-like interface that encourages non-linear workflows. A user study (N=8) demonstrated that Expandora significantly increases prompt diversity, the number of prompts users tried within a given time, and user satisfaction compared to the baseline. Nonetheless, its limitations in supporting convergent thinking suggest opportunities for holistically improving creative processes.