The advent of large pre-trained language models has made it possible to make high-quality predictions on how to add or change a sentence in a document. However, the high branching factor inherent to text generation impedes the ability of even the strongest language models to offer useful editing suggestions at a more global or document level. We introduce a new task, DOCUMENT SKETCHING, which involves generating entire draft documents for the writer to review and revise. These drafts are built from sets of documents that overlap in form -sharing large segments of potentially reusable text -while diverging in content. To support this task, we introduce a Wikipediabased dataset of analogous documents and investigate the application of weakly supervised methods, including use of a transformer-based mixture of experts, together with reinforcement learning. We report experiments using automated and human evaluation methods and discuss relative merits of these models.