Many of the stories at the core of narrative entertainment involve a number of plot lines that combine to give them interest. The present paper sets out to solve the problem of how several different plot lines, each one of them complete in its own sense, can be combined into a single linear sequence that works reasonably well as a plot. Starting from a brief review of how existing storytelling systems address the task, a representation for plots and plot templates is proposed that allows the combination of several subplots into a single-plot line. Four strategies for weaving plots are proposed, two taken from literary studies and two computational baselines, and a formative evaluation of a set of stories produced by these solutions is presented. Finally, open issues, promising avenues of future work and the relation to previous work, are discussed.