Is it possible to install MiKTeX and TeX Live side-by-side?

MiKTeX and TeX Live can be installed in parallel if you observe the following.

bin directories should be distinct

MiKTeX and TeX Live shouldn't share the same bin directories. On Windows, this is usually not an issue.

On Mac/Linux, you can run this test before installing MiKTeX:

tlmgr=$(which tlmgr)
if [ -z $tlmgr ]; then
    echo TeX Live is not installed
    echo OK to install MiKTeX for yourself or system-wide
elif [ "$(dirname "$tlmgr")" == "/usr/local/bin" ]; then
    echo OK to install MiKTeX for yourself
elif [ "$(dirname "$tlmgr")" == "~/bin" ]; then
    echo OK to install MiKTeX system-wide
else
    echo OK to install for yourself or system-wide
fi

Switching between MiKTeX and TeX Live

You have to adjust the environment variable PATH in order to switch between MiKTeX and TeX Live. Alternatively, you can use absolute path names.