This study examines the effect that dipole-dipole charge interactions between fractal aggregates have on the growth of dust grains. Aggregates in a plasma or radiative environment will have charge distributed over their extended surface, which leads to a net dipole moment for the charged grains. A self-consistent N-body code is used to model the dynamics of interacting charged aggregates. The aggregates are free to rotate due to collisions and dipole-dipole electrostatic interactions. These rotations are important in determining the growth rate and subsequent geometry (fractal dimension) of the grains. In contrast to previous studies which have only taken charge-dipole interactions into account, like-charged grains are found to coagulate more efficiently than neutral grains due to preferential incorporation of small aggregates into mid-sized aggregate structures. The charged aggregates tend to be more compact than neutral aggregates, characterized by slightly higher fractal dimensions.