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Four-top production is the rarest process measured at the LHC, and its complexity makes precise theoretical predictions challenging. In this talk I will show how resumming soft-gluon effects allows us to go beyond fixed-order calculations. After discussing the challenges of invariant-mass threshold resummation in processes with six coloured legs, I will present results for the invariant-mass distribution and total cross section at improved next-to-leading logarithmic accuracy, including non-logarithmic O(\alpha_s) terms (NLL’ accuracy). Our predictions modify the fixed-order invariant-mass distribution and significantly reduce theoretical uncertainties.