How much does "overall site semantic theme" influence rankings?

[bjs2010]

OK.

I've optimized sites before that are dedicated to 1, 2 or 3 products and or services. These sites inherently talk about one main thing - so the semantics of the content across the whole site reflect this. I get these ranked well on a local level.

Now, take  an e-commerce site - which I am working on - 2000 products, all of which are quite varied - cookware, diningware, art, decor, outdoor, appliances... there is a lot of different semantics throughout the site's different pages.

Does this influence the ranking possibilities?

Your opinion and time is appreciated. Thanks in advance.

[IOSC]

I think that it is tough to answer the question posed in title of your post other than to say "a lot".  But I don't think that having a tight "overall site semantic theme" and selling a lot of products are mutually exclusive.

For instance, Home Depot's Title Tag is "Home Improvement Made Easy with New Lower Prices", so that is a massive site where essentially everything is tailored towards fulfilling that one idea, which is extremely broad.

Drill down to product descriptions and they describe individual products and their usefulness in the context of the rest of the home/ other products that they sell.