The $\mathcal A$-classification of multigerm singularities is discussed, based on the theory of complete transversals. An $\mathcal A$-classification of $r$-multigerms from the plane to 3-space of $\mathcal A-\text{codimension} \leq 6-r$ is carried out and the bifurcation geometry of these singularities analysed. This work has applications to the study of two-dimensional spatial motions, giving local models for the singularities which appear on general trajectories of rigid body motions from the plane to 3-space. In addition, our classification is extensive enough to give the full list of simple multigerm singularities from the plane to 3-space.
