Got a 0x8070666 "Setup Failed - another version installed" popup message when installing 3.6.3 with 3.6.4 and 3.5.1 already installed (all are "just for me" installs). The problem is independent of word length.
It should be possible to install any/every earlier version (within reason) provided the earlier version is "virtualized" by being placed in it's own folder (which I was what I was doing). 
Please accomodate this capability as it is often needed to support users using earlier versions of Python. 

Environment: 64 bit Win7 Enterprise SP1 on a IM controlled machine. Possible red herring: IM recently upgraded java on this machine to "1.8.0_151".  32 and 64 bit versions of all releases are installed on this machine.

This is a big feature request, as our current installer technology is specifically designed for ease of upgrading between minor versions (e.g. 3.6.3->3.6.4). We would need to completely rewrite our installers.

If you want to avoid the installers completely and have partially isolated instances, consider the packages on nuget.org (see https://www.nuget.org/packages?q=publisher%3A%22Python+Software+Foundation%22 ). Note that these may break if you have installed a similar (same x.y) version of Python using the installer, but won't have any trouble if you have used Nuget to install all the versions on your machine.

For fully isolated instances, you can add a "python._pth" file to these after they have been extracted (or a pyvenv.cfg with applocal=1 for Python 3.5). This will suppress all registry lookups that may be confused by normal installs, as well as environment variables and optionally user site packages and .pth files.

> The problem is independent of word length.

There should be no problem installing 3.6.4 of one architecture and 3.6.3 of the other at the same time. I myself do this all the time with every version of Python. You can't do it if they are the same architecture.

Please confirm that this particular scenario does not work, and provide log files for both the successful and the failed install. There may be an issue specific to your environment that we can help diagnose.

We confirmed offline that it's not a bug.