Assign multiple taxonomies to one post

I have created CPT called "Pharmacy" which have a lot of pharmacies inside (approx 10.000)

Pharmacies offer 2 different services (skin & scalp) and some provide both services but some provide only one.

What I am trying to add is skin & scalp as taxonomies that can be assigned to each pharmacy depending what they offer.

So let’s say that pharmacy_one offers both services then the link structure should look like this:

/skin/pharmacy_one /scalp/pharmacy_one 

Finally, these taxonomies (skin & scalp) need to be connected to custom template page-skin.php & page-scalp.php depending on the URL and display different layout.

So "pharmacy_one" needs to have 2 layout and 2 links.

Is it possible to achieve it?