Can be used the module to create a facet with the elements of 3 diferents taxonomies?

Problem/Motivation

I'm working with drupal 9.5.x

I have three taxonomies: Grandparent, Parent, and Child. The Child taxonomy has an entity reference field pointing to the Parent taxonomy, and the Parent taxonomy has an entity reference field pointing to the Grandparent taxonomy.

In the Processors tab of the search index, I have selected the following options:

Using Dependent facets, I can display Parent elements when a Grandparent is selected, and when a Parent is selected, the Child elements are displayed. What I am trying to achieve is to create a structure that behaves like a hierarchical taxonomy, where the facets would show the relationships as a hierarchy.

I'd like to now if I can use this module to build only one facet with all the elements as a herarchy taxonomy.