  The technique of sparse domination, i.e., dominating operators with sums of
averages taken over sparsely distributed cubes, has seen rapid development
recently within the realms of harmonic analysis. A useful extension of sparse
domination called convex body domination allows one to estimate operators in
matrix-weighted spaces. In this paper, we extend recent sparse domination
results for a class of multi-scale operators due to Beltran, Roos and Seeger to
the convex body setting and prove that this implies quantitative
matrix-weighted norm bounds for these operators and their commutators.
