"Duplicate" Site Question

Here's the scenario. I have built a website for a company that sells, let's say, Products A, B, C, D & E on thier main website. We want to build a new site dedicated only to selling product "B". We want to do this for marketing purposes as we cannot get optimized for all products on the main site (there are a few more reasons too but I'll spare you). For instance, we do well with product A, C, & E in the SE but stink with rankings related to product B. The low rankings are due to having to optimize for too many keyterms for these pages.

Now I am familiar with what a mirror site is, and I don't think I'm creating one of those. What I am doing is creating a totally new site with different copy, different graphics, layout, more product information, etc. The ONLY thing similar between the new site and the old site is going to be the logo, the product and the owner.

Is there any potential trouble here? I think not, but just wanted to double check. I know it's not cool to create two domains with the same site, but is there any problem with a spin-off site like this?

Your input is appreciated.

I'd say you'll be fine. Good luck with your new site!

I have not seen any issues doing it either. I typically don't do that with products but with services.