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We propose an explicit drift-randomised Milstein scheme for bothMcKean--Vlasov stochastic differential equations and associatedhigh-dimensional interacting particle systems with common noise. By using adrift-randomisation step in space and measure, we establish the scheme's strongconvergence rate of $1$ under reduced regularity assumptions on the driftcoefficient: no classical (Euclidean) derivatives in space or measurederivatives (e.g., Lions/Fr\'echet) are required. The main result isestablished by enriching the concepts of bistability and consistency ofnumerical schemes used previously for standard SDE. We introduce certainSpijker-type norms (and associated Banach spaces) to deal with the interactionof particles present in the stochastic systems being analysed. A discussion ofthe scheme's complexity is provided.

An explicit Milstein-type scheme for interacting particle systems and  McKean--Vlasov SDEs with common noise and non-differentiable drift  coefficients