We study the association between active galactic nuclei (AGN) and environment at scales of 0.01 − 1 h −1 Mpc in the IllustrisTNG simulated universe (specifically, the TNG100 simulation). We identify supermassive black hole (BH) pairs and multiples within scales of 0.01, 0.1, & 1 h −1 Mpc and examine their AGN activity in relation to randomly-selected pairs and multiples. The number density of BHs in TNG100 is n = 0.06 h 3 Mpc −3 at z 1.5 (n = 0.02 h 3 Mpc −3 at z = 3). About ∼ 10% and ∼ 1% of these BHs live in pairs and multiples, respectively, within 0.1 h −1 Mpc scales. We find that these systems have enhanced likelihood (up to factors of 3-6) of containing high Eddington ratio (η 0.7) AGN compared to random pairs and multiples. Conversely, the likelihood of an AGN to live in 0.1 h −1 Mpc scale BH systems is also higher (by factors ∼ 4 for η 0.7) compared to random pairs and multiples. We also estimate that ∼ 10% of ultra-hard X-ray selected AGN in TNG100 have detectable 2-10 keV AGN companions on 0.1 h −1 Mpc scales, in agreement with observations. On larger spatial scales (∼ 1 h −1 Mpc), however, no significant enhancements in AGN activity are associated with BH pairs and multiples, even at high Eddington ratios. The enhancement of AGN activity in rich, small-scale ( 0.1 h −1 Mpc) environments is therefore likely to be driven by galaxy interactions and mergers. Nonetheless, the overall percentage of AGN that live in 0.1 h −1 Mpc scale multiples is still subdominant (at most ∼ 40% for the highest Eddington ratio AGN). Furthermore, the associated enhancement in their Eddington ratios of BH systems (as well as merging BHs) is only up to factors of ∼ 2 − 3. Thus, our results support the existence of a merger-AGN connection, but they also suggest that mergers and interactions play a relatively minor role in fueling the AGN population as a whole.