Traditionally, interatomic potentials assume local bond formation supplemented by long-range electrostatic interactions when necessary. This ignores intermediate-range multiatom interactions that arise from the relaxation of the electronic structure. Here, we present the multilayer atomic cluster expansion (ml-ACE) that includes collective, semi-local multiatom interactions naturally within its remit. We demonstrate that ml-ACE significantly improves fit accuracy and efficiency compared to a local expansion on selected examples and provide physical intuition to understand this improvement.