The only Plane that currently needs six hex characters is Plane 16, Private Use Area B, and it doesn’t seem that any of the various (non-standard) registries for Private Use Area codepoints have anything yet in that range.
The bigger problem, however, is that the keyboard is limited in what it can send to the operating system to only a relatively small set of keycodes.
There are other topics that already cover this in detail, e.g. Compose key(s) in firmware.