Self-supervised learning (SSL) methods have achieved remarkable success in learning image representations by focusing on invariance — discarding transformation information that some computer vision tasks actually require. While recent approaches like SIE attempt to address this limitation by learning equivariant features using linear operators in feature space, they impose restrictive assumptions that constrain flexibility and generalization. We introduce a novel SSL auxillary task that learns equivariant-coherent representations through intermediate transformation reconstruction, which can be integrated with existing augmentation-based SSL methods. Our key idea is to reconstruct images at intermediate points along transformation paths, e.g. when training on 30° rotations, we reconstruct the 10° and 20° rotation states. Reconstructing intermediate states uses augmentation information, rather than suppressing it, and therefore requires equivariant features carrying such information.Our method decomposes feature vectors into invariant and equivariant parts, training them with standard SSL losses and reconstruction losses, respectively. We demonstrate substantial improvements on synthetic equivariance benchmarks while maintaining competitive performance on downstream tasks requiring invariant representations. The approach seamlessly integrates with existing SSL methods (iBOT, DINOv2) and consistently enhances performance across diverse tasks, including segmentation, detection, depth estimation, and video dense prediction. Our framework provides a practical way for augmenting SSL methods with equivariant capabilities while preserving invariant performance.