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A multiple conjugation quandle is an algebra whose axioms are motivated fromhandlebody-knot theory. Any linear extension of a multiple conjugation quandlecan be described by using a pair of maps called an MCQ Alexander pair. In thispaper, we show that any affine extension of a multiple conjugation quandle canbe described by using a quadruple of maps, called an augmented MCQ Alexanderpair.

Affine extensions of multiple conjugation quandles and augmented MCQ Alexander pairs