Modern AI services must continually adapt to newly joined domains, yet delivering high-quality customized models is hampered by label sparsity, domain shifts, and tight budgets. We formulate this challenge as the learning system expansion problem and introduce HaT, an efficient heterogeneity-aware knowledge-transfer framework. HaT first selects a small set of high-quality source models with minimal overhead, and then fuses their imperfect predictions through a sample-wise attention mixer. Later, it adaptively distills the fused knowledge into target models via a knowledge dictionary. Extensive experiments on different tasks and modalities show that HaT outperforms state-of-the-art baselines by up to 16.5\% accuracy, and saves 31.1\% training time and up to 93.0\% traffic.