Please help ID this breed and skin condition :)

[jennylynncross]

I am hoping someone can help my friend identify the breed of puppy she adopted about 6 months ago. He is less than a year old and is small to midsize (although he seems as though he will stay small). ALSO: When she adopted him, he had a flaky skin condition that the shelter just attributed to needing a good bath and some skin TLC, but here it is 6 months later and this poor pupper (and his mamma) have been to the vet SEVERAL times ($$$), he’s been put on steroids, antibiotics, antifungals, specialized shampoos and regular washes, specialized diet, skin scrapes, biopsy...all of it! As far as i know, they have ruled out any autoimmune disorders (via the biopsy).

Here is a flickr link to some photos of him and his skin, paws, etc.
https://www.flickr.com/photos/157217.../shares/3945r4

There definitely seems to be a sort of hyperkeratosis thing happening with his paws...lots of excess growth there. Coat is good, but skin is consistently flaky throughout his body (including head and face), and a bit oily and slightly malodorous.

Please help us solve the mystery of this sweet boy! ❤️