In addition to Paul's advice, I have Office 2003, 2007, 2010, 2013 and 2016 all running on the same partition. I use Outlook 2016, though Outlook 2010 is file compatible, but cannot be run at the same time.
Microsoft's recommendations are incomplete regarding Word - see
Use different Word versions together for further recommendations with regard to shared resources that are better not shared.
Excel works better also if its startup folder is not shared.
In the case of Excel I would relocate the contents of the (Excel 2003) XLSTART folder to a new sub folder of the existing XLSTART -The start-up folder location is stored in the registry at
HKEY_CURRENT_USER\Software\Microsoft\Office\11.0\C ommon\Xlstart
Set the value to match the sub new folder name e.g. Office11XLSTART. That should sort out Excel 2003. Create similar sub folders and registry entries for each Office version i.e. Office12XLSTART & Office14XLSTART as appropriate.
I only use Word, Outlook and Excel so cannot comment on compatibility issues with other elements.