User blog comment:Ikosarakt1/Ideas of going past psi(K)/@comment-35470197-20200118075137/@comment-35470197-20200118090335

I note that you can extend them in some (non-unique) ways, but I am not certain whether they work as you intend. At least, I guess that you require the computability of the resulting function in FGH, but the requirement becomes highly non-trivial in any reasonable extensions.