It is possible to install and use TeX Live with binaries that are not in the original distribution. The most common case for this is when you are on a platform which the original TL distribution did not support.
Binaries for some less-common platforms are omitted from the DVD to save space, but they are available normally in a network install. So they aren't considered “custom” binaries in the sense of this page.
Nelson Beebe has made TL binaries for a vast collection of platforms, mirrored in Slovenia and Czech (also via ftp and rsync). The sets are available as compressed tar files. The parent README there gives details and scripts used.
Given a set of binaries, here are the steps to use it:
Regarding subsequent TL package updates from the net: ensure that you have wget, xz, and xzdec available in your PATH; otherwise, TL will have no way to download or decompress packages. Also, there will be no updates to the platform-specific packages in TL, since the custom platform doesn't exist in the canonical TL repository.
Therefore, you may have to manually adjust symlinks in your custom dir. Symlinks (on Unix) in the binary directories point to scripts that can run on any platform. When and if the target of a symlink changes location for whatever reason, you would need to update the symlink in your own directory.
If you want to install a second set of custom binaries (from, say, /tmp/barbin), you have to manually rename the first set, like this: