A new `intermediate_mode=` kwarg can't _default_ to `mode=` as that would flip flop the API's default behavior again and no doubt disrupt someone elses 3.7-3.10 authored code depending on it. :(

Regardless I do somewhat like `intermediate_mode=` more than the PR's existing `recursive_mode=` as it opens up more possible behaviors... Allowing `None` to mean "use `mode=`" is desirable as that'll likely be the most common case.  As I expect this to be very common, an easier to type name than intermediate_mode is desirable.  Brainstorming:

 * mid_mode?
 * submode?
 * imode?

My preference leans towards the latter names. Probably `submode=`.