Abstract: The study of scattering amplitudes has recently revealed intriguing similarities between theories whose Lagrangian formulations are quite different. In particular, it has been shown that amplitudes in a web of theories (of flavored scalars, gluons, pions, gravitons, non-linear photons…) can be constructed using only a small set of universal building blocks, generalizing the so-called double copy between gauge and gravity amplitudes. “How extended is the web of theories and their relations?” remains an open question, as well as “what is the most insightful representation of the relations?”. In this talk, I will build upon work of Cheung and Mangan, who proposed a map between the equations of motion of the different theories, thereby taking a step towards an off-shell version of the relations. I will discuss how to extend their formalism to effective field theories (EFTs) of the same degrees of freedom, and I will derive the amplitude relations which follow. Somewhat surprisingly, some of those are relations between EFT and renormalizable amplitudes.