**Abstract:**

The study of scattering amplitudes has recently revealed intriguing similarities between theories whose Lagrangians and symmetries 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. However, the complete extent of this web of theories remains an open question. In this talk, I will explore how effective field theories (EFTs) can be included in this story, building upon work of Cheung and Mangan. They proposed a map between the equations of motion of different theories, which I will extend to EFTs of the same degrees of freedom, leading to new amplitude relations. As an example, all-multiplicity amplitudes in gluon EFTs of mass dimension up to eight can be constructed from the renormalizable scattering data of gluons and scalars. Preliminary tests suggest that such relations generalize to all mass dimensions, building up a fully-resumed UV theory known to arise in the double copy of some string theories.