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Coherent scattering has recently attracted attention as a means of controlling the motion of levitated particles in three dimensions using a single optical cavity. In these systems, scattering of photons from the trapping field to a cavity mode has been used to cool all three modes of the centre-of-mass motion of levitated particles. The possibility of employing coherent scattering for more general quantum control has, however, not yet been discussed in the literature. Here, we present strategies for generating nonclassical correlations and for engineering interactions between motional modes of levitated particles using coherent scattering. We expand the theory developed by Gonzalez-Ballestero et al. to realize more general bilinear interactions in levitated optomechanics with coherent scattering. Going beyond the simple stationary picture, we introduce amplitude modulation as an important tool to modify the optomechanical interaction and discuss how it can be used to resonantly enhanced certain parts of the interaction, allowing, for example, strong one- and two-mode squeezing of motion. Our results thus show the potential of using coherent scattering for full quantum control of the motion of levitated particles.