This may work...

You can change this setting:
Tools|Options|General tab|Ignore other applications (check it)

Be aware that one side effect of having this setting checked is sometimes you
can't open a file by double clicking on it in explorer.  (toggle it back and
that should be fixed.)

This shows up for workbooks that have spaces in their name or path:
c:\my documents\excel\testworkbook.xls
or
c:\test of workbook2.xls

Cannot find C:\my, then more "Cannot find ..." messages.

It's more trouble than it's worth (for me, anyway).

If I want a second instance of excel, I'll just use:
windows start button|run
excel
then file|Open to open my file.

But I rarely want separate instances of excel.