We present a maximum-likelihood estimation algorithm for radio channel measurements exhibiting a mixture of independent Dense Multipath Components. The novelty of our approach is in the algorithms initialization using a deep learning architecture. Currently, available approaches can only deal with scenarios where a single mode is present. However, in measurements, two or more modes are often observed. This much more challenging multi-modal setting bears two important questions: How many modes are there, and how can we estimate those? To this end, we propose a Neural Net-architecture that can reliably estimate the number of modes present in the data and also provide an initial assessment of their shape. These predictions are used to initialize for gradient- and model-based optimization algorithm to further refine the estimates. We demonstrate numerically how the presented architecture performs on measurement data and analytically study its influence on the estimation of specular paths in a setting where the single-modal approach fails.