Vision Transformers have received significant attention due to their impressive performance in many vision tasks. While the token mixer or attention block has been studied in great detail, the channel mixer or feature mixing block (FFN or MLP) has not been explored in depth albeit it accounts for a bulk of the parameters and computation in a model. In this work, we study whether sparse feature mixing can replace the dense connections and confirm this with a block diagonal MLP structure that improves the accuracy by supporting larger expansion ratios. To improve the feature clusters formed by this structure and thereby further improve the accuracy, a lightweight, parameter-free, channel covariance attention (CCA) mechanism is introduced as a parallel branch during training. This design of CCA enables gradual feature mixing across channel groups during training whose contribution decays to zero as the training progresses to convergence. This allows the CCA block to be discarded during inference, thus enabling enhanced performance with no additional computational cost. The resulting $\textit{Scalable CHannEl MixEr}$ (SCHEME) can be plugged into any ViT architecture to obtain a gamut of models with different trade-offs between complexity and performance by controlling the block diagonal structure size in the MLP. This is shown by the introduction of a new family of SCHEMEformer models. Experiments on image classification, object detection, and semantic segmentation, with different ViT backbones, consistently demonstrate substantial accuracy gains over existing designs, especially under lower FLOPs regimes. For example, the SCHEMEformer establishes a new SOTA of 79.7% accuracy for ViTs using pure attention mixers on ImageNet-1K at 1.77G FLOPs.