Physical human-robot interaction (pHRI) requires robots to adapt to individual contact preferences, such as where and how much force is applied. Identifying preferences is difficult for a single contact; with whole-arm interaction involving multiple simultaneous contacts between the robot and human, the challenge is greater because different body parts can impose incompatible force requirements. In caregiving tasks, where contact is frequent and varied, such conflicts are unavoidable. With multiple preferences across multiple contacts, no single solution can satisfy all objectives--trade-offs are inherent, making prioritization essential. We present PrioriTouch, a framework for ranking and executing control objectives across multiple contacts. PrioriTouch can prioritize from a general collection of controllers, making it applicable not only to caregiving scenarios such as bed bathing and dressing but also to broader multi-contact settings. Our method combines a novel learning-to-rank approach with hierarchical operational space control, leveraging simulation-in-the-loop rollouts for data-efficient and safe exploration. We conduct a user study on physical assistance preferences, derive personalized comfort thresholds, and incorporate them into PrioriTouch. We evaluate PrioriTouch through extensive simulation and real-world experiments, demonstrating its ability to adapt to user contact preferences, maintain task performance, and enhance safety and comfort. Website: https://emprise.cs.cornell.edu/prioritouch.