The cross-section for Drell-Yan production of a vector boson has been previously calculated at next-to-next-to-leading order, supplemented by enhanced logarithmic terms associated with the threshold region. In this paper, we calculate a large set of enhanced terms associated with the colour structure C_F^3 at N^3LO, for the double real emission contribution in the quark-antiquark channel, as an expansion around the threshold region up to and including the first subleading power. We perform our

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... alculation using the method of regions, which systematically characterises all contributions according to whether the virtual gluon is (next-to) soft, collinear or hard in nature. Our results will prove useful for developing general formalisms for classifying next-to-leading power (NLP) threshold effects. They are also interesting in their own right, given that they constitute a previously unknown contribution to the Drell-Yan cross-section at O(α_s^3).