  The multi-flavor $BF$ theories in (3+1) dimensions with cubic or quartic
coupling are the simplest topological quantum field theories that can describe
fractional braiding statistics between loop-like topological excitations
(three-loop or four-loop braiding statistics). In this paper, by canonically
quantizing these theories, we study the algebra of Wilson loop and Wilson
surface operators, and multiplets of ground states on three torus. In
particular, by quantizing these coupled $BF$ theories on the three-torus, we
explicitly calculate the $\mathcal{S}$- and $\mathcal{T}$-matrices, which
encode fractional braiding statistics and topological spin of loop-like
excitations, respectively. In the coupled $BF$ theories with cubic and quartic
coupling, the Hopf link and Borromean ring of loop excitations, together with
point-like excitations, form composite particles.
