We present Analogical Networks, a model that segments 3D object scenes with analogical reasoning: instead of mapping a scene to part segments directly, our model first retrieves related scenes from memory and their corresponding part structures, and then predicts analogous part structures in the input object 3D point cloud, via an end-to-end learnable modulation mechanism. By conditioning on more than one retrieved memories, compositions of structures are predicted, that mix and match parts across the retrieved memories. One-shot, few-shot or many-shot learning are treated uniformly in Analogical Networks, by conditioning on the appropriate set of memories, whether taken from a single, few or many memory exemplars, and inferring analogous parses. We show Analogical Networks are competitive with state-of-the-art 3D segmentation transformer in many-shot settings and outperform them and existing paradigms of meta-learning and few-shot learning in few-shot scenarios. Our model successfully parses instances of novel object categories simply by expanding its memory, without any weight updates.