The classical Stein-Tomas theorem extends from the theory of linear Fourier restriction estimates for smooth manifolds to the one of fractal measures exhibiting Fourier decay. In the multilinear “smooth” setting, transversality allows for estimates beyond those implied by the linear theory. The goal of this talk is to investigate the question “how does transversality manifest itself in the fractal world?” We will show, for instance, that it could be through integrability properties of the multiple convolution of the measures involved, but that is just the beginning of the story. In the special case of Cantor-type fractals, we will construct multilinear Knapp examples through certain co-Sidon sets which, in some cases, will give more restrictive necessary conditions for a multilinear theorem to hold than those currently available in the literature. This is work in progress with Ana de Orellana (University of St. Andrews, Scotland).