Self-Supervised Learning (SSL) models have demonstrated exceptional performance in various speech tasks, particularly in low-resource and multilingual domains. Recent works show that fusing diverse SSL models could achieve superior performance compared to using one SSL model. However, fusing models increases the overall parameter size, leading to higher computational costs. We propose EFFUSE, a novel approach that uses a single SSL model to mimic the features of multiple SSL models via prediction, resulting in a lightweight framework with competitive performance. Our experiments show that EFFUSE outperforms individual SSL models in multilingual speech recognition tasks. Our best performing model achieves an average SUPERB score increase of 63.5 (6.3%) from the SSL baselines in Multilingual Speech Universal PERformance Benchmark (ML-SUPERB), while decreasing parameter size on average by 317M parameters (49%) from the fusion models.