  We revisit certain localised variants of the Bennett-Carbery-Tao multilinear
restriction theorem, recently proved by Bejenaru. We give a new proof of
Bejenaru's theorem, relating the estimates to the theory of
Kakeya-Brascamp-Lieb inequalities. Moreover, the new proof allows for a
substantial generalisation, exploiting the full power of the
Kakeya-Brascamp-Lieb theory.
