Machine learning models depend critically on feature quality, yet useful features are often scattered across multiple relational tables. Feature augmentation enriches a base table by discovering and integrating features from related tables through join operations. However, scaling this process to complex schemas with many tables and multi-hop paths remains challenging. Feature augmentation must address three core tasks: identify promising join paths that connect the base table to candidate tables, execute these joins to materialize augmented data, and select the most informative features from the results. Existing approaches face a fundamental tradeoff between effectiveness and efficiency: achieving high accuracy requires exploring many candidate paths, but exhaustive exploration is computationally prohibitive. Some methods compromise by considering only immediate neighbors, limiting their effectiveness, while others employ neural models that require expensive training data and introduce scalability limitations. We present Hippasus, a modular framework that achieves both goals through three key contributions. First, we combine lightweight statistical signals with semantic reasoning from Large Language Models to prune unpromising join paths before execution, focusing computational resources on high-quality candidates. Second, we employ optimized multi-way join algorithms and consolidate features from multiple paths, substantially reducing execution time. Third, we integrate LLM-based semantic understanding with statistical measures to select features that are both semantically meaningful and empirically predictive. Our experimental evaluation on publicly available datasets shows that Hippasus substantially improves feature augmentation accuracy by up to 26.8% over state-of-the-art baselines while also offering high runtime performance.