In cross-lingual transfer, NLP models over one or more source languages are applied to a low-resource target language. While most prior work has used a single source model or a few carefully selected models, here we consider a `massive' setting with many such models. This setting raises the problem of poor transfer, particularly from distant languages. We propose two techniques for modulating the transfer, suitable for zero-shot or few-shot learning, respectively. Evaluating on named entity recognition, we show that our techniques are much more effective than strong baselines, including standard ensembling, and our unsupervised method rivals oracle selection of the single best individual model.