We tackle the problem of meta-learning across heterogenous tasks. This problem seeks to extract and generalize transferable meta-knowledge through streaming task sets from a multi-modal task distribution. The extracted meta-knowledge can be used to create predictors for new tasks using a small number of labeled samples. Most meta-learning methods assume a homogeneous task distribution, thus limiting their generalization capacity when handling multi-modal task distributions. Recent work has shown that the generalization of meta-learning depends on the similarity of tasks in the training distribution, and this has led to many clustering approaches that aim to detect homogeneous clusters of tasks. However, these methods suffer from a significant increase in parameter complexity. To overcome this weakness, we propose a new heterogeneous meta-learning strategy that efficiently captures the multi-modality of the task distribution via modulating the routing between convolution channels in the network, instead of directly modulating the network weights. This new mechanism can be cast as a permutation learning problem. We further introduce a novel neural permutation layer based on the classical Benes routing network, which has sub-quadratic parameter complexity in the total number of channels, as compared to the quadratic complexity of the state-of-the-art Gumbel-Sinkhorn layer. We demonstrate our approach on various multi-modal meta-learning benchmarks, showing that our framework outperforms previous methods in both generalization accuracy and convergence speed.