How can I install MS Office and Visio 2016 parallel?

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Click-to-Run is the technology used to install Office 365 subscription and most versions of Office 2013 and newer. Windows Installer technology (MSI) was used to install the volume license editions of older versions of Office 2016 and older, such as Microsoft Office Professional Plus and Microsoft Office Standard.

You can't install the same version of Office products that use two different installation technologies installed on the same computer. This also applies to standalone applications like Access, Visio, Project, Skype for Business, or OneDrive for Business.

Note: In some cases, you also can't have two different versions of Click-to-Run applications on the same computer. For more information, see "Stop, you should wait to install Office 2016" error.

Uninstall the Windows Installer (MSI) version of Office

You can stay with the Windows Installer version of Office and not install the Office 365 Click-to-Run version you were trying to install. Or, do the following:

1. Follow the steps in Uninstall Office from a Windows computer to remove the Windows Installer version of Office.
2. Retry the installation of Office you were doing when you got the error message.

Source

You can install Visio 2013 alongside Office 2016(at least until Microsoft changes the installer the next time). If Visio 2013 fits your needs you can pursue this path.

But Visio 2013 is differently licensed so check if it's allowed for your desired purpose.