Large Language Models (LLMs) excel across diverse NLP tasks but remain too large for efficient on-device deployment. Although knowledge distillation offers a promising compression strategy, direct one-step distillation from a large teacher to a small student often leads to substantial performance loss due to the capacity gap. In this work, we revisit multi-step knowledge distillation (MSKD) as an effective remedy, exploring how staged, size-aware transfer paths can better preserve teacher knowledge across students of varying scales. Through extensive experiments with GPT-2 and OPT, we demonstrate that MSKD consistently improves ROUGE-L and perplexity over single-step approaches without requiring specialized fine-tuning. Our results establish multi-step transfer as a simple yet powerful framework for progressively compressing LLMs into efficient, high-performing Small Language Models (SLMs).