<p>Using invariant-mass threshold resummation, we compute the invariant-mass distribution and the total cross section for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27501_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi>t</mi> <mover accent="true"> <mi>t</mi> <mo stretchy="true">¯</mo> </mover> <mi>t</mi> <mover accent="true"> <mi>t</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( t\overline{t}t\overline{t} \)</EquationSource> </InlineEquation> production at the LHC with centre-of-mass energy of 13<i>.</i>6 TeV at NLL^′ accuracy. This accuracy includes next-to-leading logarithmic contributions together with relative 𝒪(<i>α</i>_<i>s</i>) non-logarithmic terms present in the threshold limit. We match the NLL^′ results to NLO in QCD and to complete NLO with electroweak corrections. We find that the inclusion of NLL^′ soft-gluon corrections significantly reduces the size of the theoretical uncertainties and greatly improves the convergence of the predictions when considering various choices of renormalisation and factorisation scales.</p>