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The WMS layer Change Coordinate System dialog drop-down list does not display Coordinate System names.
Some WMS services may not support any coordinate systems, in which case the drop-down list for the Change Coordinate System dialog box will be blank.
For confirmation that the WMS service does not support Coordinate Systems, check the capabilities file. This information is also displayed in the Service Properties dialog box in ArcCatalog, or in the Layer tab of the Layer Properties dialog box in ArcMap.
<a href='https://support.esri.com/en/knowledgebase/techarticles/detail/27948' target='_blank'>How To: View the WMS service capabilities</a>