Emotional support conversation systems aim to help users alleviate distress through empathetic dialogue. However, existing ESC datasets often use coarse-grained problem categories, limiting models’ ability to address users’ complex, overlapping challenges. To address this, we propose a generalizable fine-grained problem enhancement method that systematically augments problem types, user scenarios, and profiles, enabling the construction of richer and more diverse ESC corpora. As a demonstration, we construct EmoCare, a large-scale ESC dataset with 2.6K dialogues and 42.8K utterances, expanding problem type coverage from 13 to 45 fine-grained categories. Building on this data augmentation process, we introduce FPEMF, a flexible framework for empathetic dialogue generation, which comprises two modules: fine-grained problem enhancement and multi-dimensional feedback, which can be seamlessly integrated with various backbone models. The multi-dimensional feedback module evaluates responses from four perspectives: emotional understanding, strategy effectiveness, contextual consistency, and topic relevance, guiding models to generate more supportive replies. Experiments show that FPEMF consistently improves both automatic and human evaluation metrics across different models.