Ecommerce store becoming a sole distributor of a retail product

Hello! Ok, heres the situation, I've come across a task I've never ran into. I try to help with SEO for an online eCommerce store. One of the manufacturers of their most popular product came to us (this product is also being sold by all of our competitors) and decided we were to be the sole distributor of this product. This means we'll be the distributor to all of our competitors, which if weird but interesting. All of our competitors rank higher than we do in the retail space for keywords related to that product.

Now that we're the sole distributor of a product, but still required to supply product to competitors, while still trying to he competitive in their own retail online store, what steps would you suggest taking to come out on top in organic rankings for that product? Is it crazy to attempt to try having our competitors link to our page in some way naming us as one of their distributors?