Radio Frequency Fingerprinting Identification (RFFI) leverages inherent discrepancies in radiation source hardware, which are challenging to mimic and counterfeit. This attribute enhances the security of wireless networks and ensures the protection of data privacy, vital for secure communications. Inherent challenges such as channel fading and frequency drift affect radio signals. This paper explores the synergy between Automatic Modulation Recognition (AMR) and RFFI by employing a multi-label dataset to strategically influence the relationship between signal labels and individual radiation sources. We propose an advanced multi-gate mixture-of-experts convolutional neural network model, the MMOE-CNN-Transformer, which operates within a multi-task soft sharing framework. Our empirical results reveal that this model significantly enhances RFFI classification accuracy, particularly at a 0dB signal-to-noise ratio, outperforming traditional single-task learning (STL) approaches and surpassing the efficacy of hard sharing architectures, exemplified by the Shared-Bottom model. This study underscores the potential of integrating sophisticated neural network architectures in enhancing the robustness and precision of radio frequency identification systems.