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IceCube alert events are neutrinos with a moderate-to-high probability of having astrophysical origin. In this study, we analyze 11 yr of IceCube data and investigate 122 alert events and a selection of high-energy tracks detected between 2009 and the end of 2021. This high-energy event selection (alert events + high-energy tracks) has an average probability of ≥0.5 of being of astrophysical origin. We search for additional continuous and transient neutrino emission within the high-energy events’ error regions. We find no evidence for significant continuous neutrino emission from any of the alert event directions. The only locally significant neutrino emission is the transient emission associated with the blazar TXS 0506+056, with a local significance of 3σ, which confirms previous IceCube studies. When correcting for 122 test positions, the globalp-value is 0.156 and compatible with the background hypothesis. We constrain the total continuous flux emitted from all 122 test positions at 100 TeV to be below 1.2 × 10⁻¹⁵(TeV cm²s)⁻¹at 90% confidence assuming anE⁻²spectrum. This corresponds to 4.5% of IceCube’s astrophysical diffuse flux. Overall, we find no indication that alert events in general are linked to lower-energetic continuous or transient neutrino emission.