Source-Free Domain Adaptation (SFDA) seeks to adapt a source model, which is pre-trained on a supervised source domain, for a target domain, with only access to unlabeled target training data. Relying on pseudo labeling and/or auxiliary supervision, conventional methods are inevitably error-prone. To mitigate this limitation, in this work we for the first time explore the potentials of off-the-shelf vision-language (ViL) multimodal models (e.g., CLIP) with rich whilst heterogeneous knowledge. We find that directly applying the ViL model to the target domain in a zero-shot fashion is unsatisfactory, as it is not specialized for this particular task but largely generic. To make it task-specific, we propose a novel DIFO++ approach. Specifically, DIFO++ alternates between two steps during adaptation: (i) Customizing the ViL model by maximizing the mutual information with the target model in a prompt learning manner, (ii) Distilling the knowledge of this customized ViL model to the target model, centering on gap region reduction. During progressive knowledge adaptation, we first identify and focus on the gap region, where enclosed features are entangled and class-ambiguous, as it often captures richer task-specific semantics. Reliable pseudo-labels are then generated by fusing predictions from the target and ViL models, supported by a memory mechanism. Finally, gap region reduction is guided by category attention and predictive consistency for semantic alignment, complemented by referenced entropy minimization to suppress uncertainty. Extensive experiments show that DIFO++ significantly outperforms the state-of-the-art alternatives. Our code and data are available at https://github.com/tntek/DIFO-Plus.