Recent advancements in multilingual automatic speech recognition (ASR) have been driven by large-scale end-to-end models like Whisper. However, challenges such as language interference and expanding to unseen languages (language expansion) without degrading performance persist. This paper addresses these with three contributions: 1) Entire Soft Prompt Tuning (Entire SPT), which applies soft prompts to both the encoder and decoder, enhancing feature extraction and decoding; 2) Language-Aware Prompt Tuning (LAPT), which leverages cross-lingual similarities to encode shared and language-specific features using lightweight prompt matrices; 3) SPT-Whisper, a toolkit that integrates SPT into Whisper and enables efficient continual learning. Experiments across three languages from FLEURS demonstrate that Entire SPT and LAPT outperform Decoder SPT by 5.0% and 16.0% in language expansion tasks, respectively, providing an efficient solution for dynamic, multilingual ASR models with minimal computational overhead.