State of the art speech enhancement (SE) models achieve strong performance on neurotypical speech, but their effectiveness is substantially reduced for pathological speech. In this paper, we investigate strategies to address this gap for both predictive and generative SE models, including i) training models from scratch using pathological data, ii) finetuning models pretrained on neurotypical speech with additional data from pathological speakers, and iii) speaker specific personalization using only data from the individual pathological test speaker. Our results show that, despite the limited size of pathological speech datasets, SE models can be successfully trained or finetuned on such data. Finetuning models with data from several pathological speakers yields the largest performance improvements, while speaker specific personalization is less effective, likely due to the small amount of data available per speaker. These findings highlight the challenges and potential strategies for improving SE performance for pathological speakers.