  We find all solutions to the constant Yang--Baxter equation
$R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}$ in three dimensions, subject to an
additive charge-conservation ansatz. This ansatz is a generalisation of
(strict) charge-conservation, for which a complete classification in all
dimensions was recently obtained. Additive charge-conservation introduces
additional sector-coupling parameters -- in 3 dimensions there are $4$ such
parameters. In the generic dimension 3 case, in which all of the $4$ parameters
are nonzero, we find there is a single 3 parameter family of solutions. We give
a complete analysis of this solution, giving the structure of the centraliser
(symmetry) algebra in all orders. We also solve the remaining cases with three,
two, or one nonzero sector-coupling parameter(s).
