> 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.