  Tri-boson production together with vector-boson scattering is a privileged
channel to study the electroweak structure of the Standard Model. Upcoming LHC
running stages will allow to measure these processes at unprecedented accuracy
and for all possible final states, which requires to push theory predictions to
still unexplored frontiers. In this work we present the first calculation for
the process ${\rm p}{\rm p}\to\mu^+\mu^-{\rm e}^+\nu_{\rm e}\,{\rm j}\,{\rm j}$
at the LHC in a tri-boson phase space. We evaluate the three LO contributions,
namely the $\mathcal{O}(\alpha^6)$, which contains the genuine tri-boson
signature, along with the $\mathcal{O}(\alpha_{\rm s}\alpha^5)$ and
$\mathcal{O}(\alpha_{\rm s}^2\alpha^4)$, and the two $\mathcal{O}(\alpha^7)$
and $\mathcal{O}(\alpha_{\rm s}\alpha^6)$ NLO corrections. The calculation is
based on full Standard-Model matrix elements, including all resonant and
non-resonant terms, complete spin correlations and interference effects.
Integrated and differential cross sections are presented for a fiducial region
inspired by High Luminosity LHC prospect studies. We find electroweak
corrections of $-14\%$ for the fiducial cross section, almost twice as large as
for other tri-boson processes.
