  We study the phase transition between the Coulomb liquid and the columnar
crystal in the 3D classical dimer model, which was found to be continuous in
the O(3) universality class. In addition to nearest neighbor interactions which
favor parallel dimers, further neighbor interactions are allowed in such a
manner that the cubic symmetry of the original system remains intact. We show
that the transition in the presence of weak additional, symmetry preserving
interactions is first-order. However the universality class of the transition
remains continuous when the additional interactions are weakly repulsive. In
this way, we verify the existence of a multicritical point near the unperturbed
transition and we identify a critical line of unconventional transitions
between the Coulomb liquid phase and the $6-$fold columnar phase.
