  Modern global analyses of the structure of the proton include collider
measurements which probe energies well above the electroweak scale. While these
provide powerful constraints on the parton distribution functions (PDFs), they
are also sensitive to beyond the Standard Model (BSM) dynamics if these affect
the fitted distributions. Here we present a first simultaneous determination of
the PDFs and BSM effects from deep-inelastic structure function data by means
of the NNPDF framework. We consider representative four-fermion operators from
the SM Effective Field Theory (SMEFT), quantify to which extent their effects
modify the fitted PDFs, and assess how the resulting bounds on the SMEFT
degrees of freedom are modified. Our results demonstrate how BSM effects that
might otherwise be reabsorbed into the PDFs can be systematically disentangled.
