Kinematic couplings are used when two rigid bodies need to be repeatedly and accurately positioned with respect to each other. They allow for sub-micron positioning repeatability by suppressing play and reducing strains in the bodies. Typical applications are in astronomy, semiconductors and metrology. This work generalizes two-body kinematic couplings to multi-body kinematic mounts with a focus on the 3-body case. This work presents a complete analysis of the 3-body case by providing a novel set of representative examples, realized demonstrators, and applications of 3-body kinematic mounts.