Unable to drag and drop web parts onto classic pages in SharePoint Online
Summary
When you try to drag and drop a web parts within or across Web Part Zones using modern browsers on Classic Pages in SharePoint Online, the Web Part doesn't move.
More information
As a workaround, use Internet Explorer 10 in document mode. For more information, see Display a classic SharePoint Online site in Internet Explorer 10 document mode.
Microsoft is researching this problem and will post more information as it becomes available.
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