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A search for the flavor-changing neutral-current decay B+ →K+$ν\bar{ν}$ is performed at the Belle II experiment at the SuperKEKB asymmetric energy electron-positron collider. The data sample corresponds to an integrated luminosity of 63 fb-1 collected at the Υ (4S) resonance and a sample of 9 fb-1 collected at an energy 60 MeV below the resonance. Because the measurable decay signature involves only a single charged kaon, a novel measurement approach is used that exploits not only the properties of the B+ →K+$ν\bar{ν}$ decay, but also the inclusive properties of the other B meson in the Υ(4S) $B\bar{B}$ event, to suppress the background from other B meson decays and light-quark pair production. This inclusive tagging approach offers a higher signal efficiency compared to previous searches. No significant signal is observed. An upper limit on the branching fraction of B+ →K+$ν\bar{ν}$ of 4.1 × 10-5 is set at the 90% confidence level.