Four-fermion interactions are important in many areas of particle physics, from effective descriptions of weak interactions and QCD to parametrisations of BSM physics in frameworks such as SMEFT. In lower dimensional (2+1) QFTs, four-fermion operators can UV complete themselves when strong coupling effects generate interacting RG fixed points. In this talk, I will explain how these special circumstances carry over to 3+1 dimensions. Using a toy “EFT” containing many flavours N of Dirac fermion, and the toolbox of the large-N expansion, I will demonstrate that four-fermion interactions are able to UV complete themselves via strongly coupled RG fixed points, that this corresponds to formal renormalisability in the large-N expansion, and that ultimately physical predictions in this theory are fully determined in terms of just three parameters. Along the way, I will discuss the systematics of renormalisation, and the required structure of counterterms, and show how scattering amplitudes undergo a crossover from the EFT regime in the IR to a near-conformal UV with large operator anomalous dimensions.