I have a company that runs multiple ecommerce brands. I'm interested in starting a new project, but I would like to run this new business under my current company (like a DBA).

For this new project, I'm interested to partner with someone and profit share with them ONLY on this project and NOT on my other ecommerce brands. Meaning, I don't want them to have share of my existing company nor share of my ecommerce brands I built myself.

Honestly I'm confused about the formalities of this and whether this is appropriate or not. Your advice will be greatly appreciated on how to get this sorted, like what kind of contract to prepare etc.