This paper describes an extension to the constraint satisfaction problem (CSP) approach called MUSE CSP (Multiply SEgmented Constraint Satisfaction Problem). This extension is especially useful for those problems which segment into multiple sets of partially shared variables. Such problems arise naturally in signal processing applications including computer vision, speech processing, and handwriting recognition. For these applications, it is often difficult to segment the data in only one way given the low-level information utilized by the segmentation algorithms. MUSE CSP can be used to efficiently represent several similar instances of the constraint satisfaction problem simultaneously. If multiple instances of a CSP have some common variables which have the same domains and compatible constraints, then they can be combined into a single instance of a MUSE CSP, reducing the work required to enforce node and arc consistency.