For many biomedical modelling tasks a number of different types of data may influence predictions made by the model. An established approach to pursuing supervised learning with multiple types of data is to encode these different types of data into separate kernels and use multiple kernel learning. In this paper we propose a simple iterative approach to multiple kernel learning (MKL), focusing on multi-class classification. This approach uses a block L1 -regularization term leading to a jointly convex formulation. It solves a standard multi-class classification problem for a single kernel, and then updates the kernel combinatorial coefficients based on mixed RKHS norms. As opposed to other MKL approaches, our iterative approach delivers a largely ignored message that MKL does not require sophisticated optimization methods while keeping competitive training times and accuracy across a variety of problems. We show that the proposed method outperforms state-of-the-art results on an i...