Traditional image clustering techniques only find a single grouping within visual data. In particular, they do not provide a possibility to explicitly define multiple types of clustering. This work explores the potential of large vision-language models to facilitate alternative image clustering. We propose Text-Guided Alternative Image Consensus Clustering (TGAICC), a novel approach that leverages user-specified interests via prompts to guide the discovery of diverse clusterings. To achieve this, it generates a clustering for each prompt, groups them using hierarchical clustering, and then aggregates them using consensus clustering. TGAICC outperforms image- and text-based baselines on four alternative image clustering benchmark datasets. Furthermore, using count-based word statistics, we are able to obtain text-based explanations of the alternative clusterings. In conclusion, our research illustrates how contemporary large vision-language models can transform explanatory data analysis, enabling the generation of insightful, customizable, and diverse image clusterings.