Most information extraction methods focus on binary relations expressed within single sentences. In high-value domains, however, $n$-ary relations are of great demand (e.g., drug-gene-mutation interactions in precision oncology). Such relations often involve entity mentions that are far apart in the document, yet existing work on cross-sentence relation extraction is generally confined to small text spans (e.g., three consecutive sentences), which severely limits recall. In this paper, we propose a novel multiscale neural architecture for document-level $n$-ary relation extraction. Our system combines representations learned over various text spans throughout the document and across the subrelation hierarchy. Widening the systems purview to the entire document maximizes potential recall. Moreover, by integrating weak signals across the document, multiscale modeling increases precision, even in the presence of noisy labels from distant supervision. Experiments on biomedical machine reading show that our approach substantially outperforms previous $n$-ary relation extraction methods.