Real-world radar signals are frequently corrupted by various artifacts, including sensor noise, echoes, interference, and intentional jamming, differing in type, severity, and duration. This pilot study introduces a novel model, called Co-Operational Regressor Network (CoRe-Net) for blind radar signal restoration, designed to address such limitations and drawbacks. CoRe-Net replaces adversarial training with a novel cooperative learning strategy, leveraging the complementary roles of its Apprentice Regressor (AR) and Master Regressor (MR). The AR restores radar signals corrupted by various artifacts, while the MR evaluates the quality of the restoration and provides immediate and task-specific feedback, ensuring stable and efficient learning. The AR, therefore, has the advantage of both self-learning and assistive learning by the MR. The proposed model has been extensively evaluated over the benchmark Blind Radar Signal Restoration (BRSR) dataset, which simulates diverse real-world artifact scenarios. Under the fair experimental setup, this study shows that the CoRe-Net surpasses the Op-GANs over a 1 dB mean SNR improvement. To further boost the performance gain, this study proposes multi-pass restoration by cascaded CoRe-Nets trained with a novel paradigm called Progressive Transfer Learning (PTL), which enables iterative refinement, thus achieving an additional 2 dB mean SNR enhancement. Multi-pass CoRe-Net training by PTL consistently yields incremental performance improvements through successive restoration passes whilst highlighting CoRe-Net ability to handle such a complex and varying blend of artifacts.