  We study Yangian-invariant deformations of scattering amplitudes in 4d N=4
supersymmetric Yang-Mills theory and 3d N=6 Aharony-Bergman-Jafferis-Maldacena
(ABJM) theory. In particular, we obtain the deformed Grassmannian integral for
4d N=4 super Yang-Mills theory, both in momentum and momentum-twistor space.
For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We
investigate general deformations of on-shell diagrams, and find the deformed
Grassmannian integral for this theory. We furthermore introduce the algebraic
R-matrix construction of deformed Yangian invariants for ABJM theory.
