Efficiently transferring Learned Image Compression (LIC) model from human perception to machine perception is an emerging challenge in vision-centric representation learning. Existing approaches typically adapt LIC to downstream tasks in a single-task manner, which is inefficient, lacks task interaction, and results in multiple task-specific bitstreams. To address these limitations, we propose an asymmetric adaptor framework that supports multi-task adaptation within a single model. Our method introduces a shared adaptor to learn general semantic features and task-specific adaptors to preserve task-level distinctions. With only lightweight plug-in modules and a frozen base codec, our method achieves strong performance across multiple tasks while maintaining compression efficiency. Experiments on the PASCAL-Context benchmark demonstrate that our method outperforms both Fully Fine-Tuned and other Parameter Efficient Fine-Tuned (PEFT) baselines, and validating the effectiveness of multi-vision transferring.