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Abstract We chose the μ-term extended next-to-minimal supersymmetric standard model (μNMSSM) for this work, and we perform a phenomenological study based on the assumption that the observed Standard Model (SM)-like Higgs is explained by the presence of a double overlapping resonance and in light of the recent (g − 2) μ result. The study also takes into account a variety of experimental results, including Dark Matter (DM) direct detections and results from sparticle searches at the Large Hadron Collider (LHC). We study the properties of DM confronted with the limits from DM direct detections. As a second step, we focus our attention on the properties of the mass-degenerate SM-like Higgs bosons and on explaining the anomaly of (g −2) μ . We conclude that the anomaly of (g −2) μ can be explained in the scenario with two mass-degenerate SM-like Higgs, and there are samples that meet the current constraints and fit 1 − σ anomalies of Higgs data.