Fast ( $\mathrm{V}_{\mathrm{CME}} > 1000\text{ km}\,\text{s}^{-1}$ ) coronal mass ejections (CMEs) capable of accelerating protons beyond 300 MeV are thought to trigger hours-long sustained $\gamma $ -ray emission (SGRE) after the impulsive flare phase. Meanwhile, CME-CME interactions can cause enhanced proton acceleration, increasing the fluxes of solar energetic particles. This study explores the role of fast CME interactions in SGRE production during CME clusters, which we define as a series of CMEs linked to > C-class flares with waiting times < 1 day from the same active region (AR). We focus on clusters in major CME-productive ARs (major ARs), by defining a major AR as one that produced > 1 CME associated to a major (> M-class) flare. The study identified 76 major ARs between 2011 and 2019, of which 12 produced all SGRE events. SGRE-producing ARs exhibit higher median values for the speed of their fastest CMEs (2013 vs. 775 km s−1) and the class of their strongest flares (X1.8 vs. M5.8), compared to SGRE-lacking ARs. They also produced relatively faster CMEs (median speed: 1418 vs. 1206.5 km s−1), with the SGRE-associated CMEs occurring during periods of higher CME rates than typical fast CME epochs. Twelve of 22 (54.5%) SGRE events and 5 of 7 (71.4%) long-duration (> 10 h) SGRE events occurred during CME clusters, with high chances of CME-CME interactions. A case study on very active major ARs showed that all SGRE-associated CMEs with $\mathrm{V}_{\mathrm{CME}} \lesssim 2000\text{ km}\,\text{s}^{-1}$ underwent CME-CME interactions within ≲ 10 ${\mathrm{R_{\odot }}}$ , while SGRE-associated CMEs faster than 3000 km s−1 did not undergo interactions.
