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Nb₃Sn is a promising next-generation material for superconducting radiofrequency cavities, with significant potential for both large scale and compact accelerator applications. However, so far, Nb₃Sn cavities have been limited to continuous wave accelerating fields <18 MV m⁻¹. In this paper, new results are presented with significantly higher fields, as high as 24 MV m⁻¹in single cell cavities. Results are also presented from the first ever Nb₃Sn-coated 1.3 GHz 9-cell cavity, a full-scale demonstration on the cavity type used in production for the European XFEL and LCLS-II. Results are presented together with heat dissipation curves to emphasize the potential for industrial accelerator applications using cryocooler-based cooling systems. The cavities studied have an atypical shiny visual appearance, and microscopy studies of witness samples reveal significantly reduced surface roughness and smaller film thickness compared to typical Nb₃Sn films for superconducting cavities. Possible mechanisms for increased maximum field are discussed as well as implications for physics of RF superconductivity in the low coherence length regime. Outlook for continued development is presented.