  The various formulations of scattering amplitudes presented in recent years
have underlined a hidden unity among very different theories. The KLT and BCJ
relations, together with the CHY formulation, connect the S-matrices of a wide
range of theories: the transmutation operators, recently proposed by Cheung,
Shen and Wen, provide an account for these similarities. In this note we use
the transmutation operators to link the various CHY integrands at tree-level.
Starting from gravity, we generate the integrands for Yang-Mills, biadjoint
scalar, Einstein-Maxwell, Yang-Mills scalar, Born-Infeld, Dirac-Born-Infeld,
non-linear sigma model and special Galileon theories, as well as for their
extensions. We also commence the study of the CHY-like formulae at loop level.
