If there is, it is still a MS "top secret".
Have you RECENTLY tried installing project 2013 now that you have 2016 installed. Over the last few months a few people have reported being able to mix Office version installations (including 2016):
Supported scenarios for installing different versions of Office, Visio, and Project on the same computer– Different Years and MSI vs CTR.
https://technet.microsoft.com/library/mt712177%28v=office.16%29.aspx?f=255&MSPPError=-2147217396
Visio and Project versions that can be installed on the same computer with Office 365 ProPlus
https://technet.microsoft.com/en-us/library/mt422981.aspx
2016 Visio CTR/MSI installation options:
http://answers.microsoft.com/en-us/msoffice/forum/msoffice_install-mso_win10/fail-to-install-visio-2016-std-mak-with-e3-office/b9718224-7e82-4208-948f-564989039798?msgId=9f1114a1-326d-4946-8f4f-314dcd4c55d3
Felix, a MS employee posted the following chart and suggestion:
<snip>
As the Visio 2016 MAK client is MSI Version, it can’t be installed with Office 2016(Click-To-Run) provided by Office 365.
Version Visio 2016 CTR Visio 2016 MSI
Office 2016 CTR
YES NO
Office 2016 MSI
NO
YES
Office 2013 CTR
YES YES
Office 2013 MSI
YES
YES