  Topological entanglement structure amongst disjoint torus boundaries of three
manifolds have already been studied within the context of Chern-Simons theory.
In this work, we study the topological entanglement due to interaction between
the quasiparticles inside three-manifolds with one or more disjoint $S^2$
boundaries in SU($N$) Chern-Simons theory. We focus on the world-lines of
quasiparticles (Wilson lines), carrying SU($N$) representations, creating four
punctures on every $S^2$. We compute the entanglement entropy by partial
tracing some of the boundaries. In fact, the entanglement entropy depends on
the SU($N$) representations on these four-punctured $S^2$ boundaries. Further,
we observe interesting features on the GHZ-like and W-like entanglement
structures. Such a distinction crucially depends on the multiplicity of the
irreducible representations in the tensor product of SU($N$) representations.
