Permalinks for custom post type taxonomies with children

I have looked around a number of places for this but can’t seem to lock down the proper solution.

I’d like to setup a permalink structure such that I have:

abc.com/custom-post-type/taxonomy-parent/taxonomy-child/post-name

For example, let’s say I’m making a research website and I’ve got a custom post type called “trials”, with a custom taxonomy of “trial_categories” that includes parents and children. So I may have a post with “Experiment ABC123” which is a custom taxonomy of “cancer” (parent) and “lung” (child).

I’d like to have a permalink of abc.com/trials/cancer/lung/experiment-abc123

Is this possible??

I can post the code for the custom post type I registered if it helps.