In reply to Pullhard:
Starting Excel with the flag "/x" on the command line will open a new instance of Excel, separate from the one you already have running. This option works for Excel 2013 and 2016.
Just create a shortcut to the Excel executable on your desktop or taskbar, something like this for the 32 bit version of Excel 2016:
"C: | Program Files (x86) | Microsoft Office | Office16 | EXCEL.EXE" /x
Click / double-click the shortcut when you want to open a new Excel instance while your macro is running.
Edit: Apparently backslashes are not allowed here - replace the " | " with backslashes
Post edited at 17:20