Amplituhedra are a family of spaces with the property that co-dimension one boundary of an Amplituhedron are the product of "smaller" Amplituhedra. In addition they are given a volume form that has a singularity on these boundaries, and whose residue over these boundaries is the product of the volume forms of the Amplituhedra factorizing the boundaries.
The volume form is localized to a point which reaches the boundary only if the external data are becoming singular, in the sense of amplitudes (in momentum-twistor space, if four of them becomes linear dependent).
It seems to me that this is the bone-idea of the Amplituhedron, and this seems very similar to trying to compute amplitudes by principles (locality, unitarity...). Put in other words, isn't the problem of extending the Amplituhedron formalism to other theories more or less equivalent to the problem of substituting a quantum field theory with a S-matrix theory?
EDIT: To be more specific: Does the amplituhedron works exactly only for those theories where the scattering amplitudes can be fixed as the only functions with the right poles and factorization properties?