End-to-end backpropagation remains the dominant training paradigm in deep learning, yet it suffers from inherent drawbacks, including update locking, high GPU memory consumption, and limited biological plausibility. Supervised local learning alleviates these issues by dividing the network into multiple blocks and training each block independently with an auxiliary network. However, gradient isolation also weakens the influence of downstream representations on earlier blocks, often resulting in a clear accuracy gap to end-to-end training. We propose Momentum Auxiliary Network++ (MAN++), a scalable framework that improves supervised local learning via a lightweight parameter-space transfer between adjacent blocks. MAN++ employs the exponential moving average (EMA) of parameters from adjacent blocks to propagate contextual information across the network. To address feature mismatches arising from direct EMA parameter transfer, we introduce a learnable scaling bias, which compensates feature statistics mismatch and stabilizes the transfer. Extensive experiments on image classification, object detection, and semantic segmentation across multiple architectures illustrate that MAN++ achieves accuracy on par with end-to-end training while substantially reducing GPU memory usage. These results position MAN++ as a practical and effective alternative to conventional backpropagation, offering new insights into scalable supervised local learning for vision tasks.