In recent years, multi-task prompt tuning has garnered considerable attention for its inherent modularity and potential to enhance parameter-efficient transfer learning across diverse tasks. This paper aims to analyze and improve the performance of multiple tasks by facilitating the transfer of knowledge between their corresponding prompts in a multi-task setting. Our proposed approach decomposes the prompt for each target task into a combination of shared prompts (source prompts) and a task-specific prompt (private prompt). During training, the source prompts undergo fine-tuning and are integrated with the private prompt to drive the target prompt for each task. We present and compare multiple methods for combining source prompts to construct the target prompt, analyzing the roles of both source and private prompts within each method. We investigate their contributions to task performance and offer flexible, adjustable configurations based on these insights to optimize performance. Our empirical findings clearly showcase improvements in accuracy and robustness compared to the conventional practice of prompt tuning and related works. Notably, our results substantially outperform other methods in the field in few-shot settings, demonstrating superior performance in various tasks across GLUE benchmark, among other tasks. This achievement is attained with a significantly reduced amount of training data, making our method a promising one for few-shot settings.