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Entity resolution, a longstanding problem of data cleaning and integration, aims at identifying data records that represent the same real-world entity. Existing approaches treat entity resolution as a universal task, assuming the existence of a single interpretation of a real-world entity and focusing only on finding matched records, separating corresponding from non-corresponding ones, with respect to this single interpretation. However, in real-world scenarios, where entity resolution is part of a more general data project, downstream applications may have varying interpretations of real-world entities relating, for example, to various user needs. In what follows, we introduce the problem of multiple intents entity resolution (MIER), an extension to the universal (single intent) entity resolution task. As a solution, we propose FlexER, utilizing contemporary solutions to universal entity resolution tasks to solve multiple intents entity resolution. FlexER addresses the problem as a multi-label classification problem. It combines intent-based representations of tuple pairs using a multiplex graph representation that serves as an input to a graph neural network (GNN). FlexER learns intent representations and improves the outcome to multiple resolution problems. A large-scale empirical evaluation introduces a new benchmark and, using also two well-known benchmarks, shows that FlexER effectively solves the MIER problem and outperforms the state-of-the-art for a universal entity resolution.