<p>We investigate the topological entanglement entropy of quantum states arising in the context of three-dimensional Chern-Simons theory with compact gauge group <i>G</i> and Chern-Simons level <i>k</i>. We focus on the quantum states associated with the <i>T</i>_{<i>dm</i>,<i>dn</i>} torus link complements, which is a <i>d</i>-party pure quantum state, and analyze its large-party limit, i.e., <i>d</i> → ∞ limit. We show that the entanglement measures in this limit will receive contributions only from the Abelian anyons, and non-Abelian sectors are suppressed in the large-party limit. Consequently, the large-party limiting value of the entanglement entropy has an upper bound of ln |<i>Z</i>_<i>G</i>|, where |<i>Z</i>_<i>G</i>| is the order of the center of the group <i>G</i>. As an explicit example, we perform quantitative analysis for the simplest case of the SU(2) group and <i>T</i>_{<i>d</i>,<i>dn</i>} torus link to obtain the large-party limit of the entanglement entropy. We further investigate the semiclassical (<i>k</i> → ∞) limit of the entropies after taking the large-party limit for this particular example.</p>