  We describe the calculation of the QCD contribution to same-sign $W$-pair
production, $pp\to e^\pm \nu_e \mu^\pm \nu_\mu jj$, resumming all contributions
scaling as $\alpha_W^4 \alpha_s^{2+k}\log^k(\hat s/p_\perp^2)$
[arXiv:2107.06818]. These leading logarithmic contributions are enhanced by
typical cuts used for Vector Boson Scattering (VBS) studies. We show that while
the cross sections are little affected by these corrections, other more
exclusive observables relevant for experimental studies are affected more
significantly.
