From my research google gives your domain an overall keyword relevancy.... lets say you have a website about "red shoes" with 20 unique pages of content about "red shoes" , and then you throw 30 pages about "purple dogs" your overall keyword relevancy for red shoes will drop...in result your google search results will not be as good.... Someone that really knows their SEO please correct me if I am wrong....
Let's use a real site, for instance, redenvelope.com and use Google. It shows up #1 for the term red envelope. It shows up #1 for the term luxury gifts. It shows up #4 for the term personalized gifts (for me). It shows up #6 for the term unique gifts (for me). Do they sell red envelopes? None that I could find. Do they sell gifts? Yes they do. So, it seems that even if your domain name has relevant keywords, it won't affect your results because most of the relevant keywords will be from the content of the webpage(s). If Google gave more relevancy to the keywords in the domain name, then you could just register very descriptive domain names with or without dashes and it would rank higher. It's been said that Google favors keywords in domain names, but how much relvancy Google puts on a domain name is unknown. It also could favor keywords in the URL itself. I say that it would not affect your results because those pages are relevant to certain keywords while other pages are relevant to other keywords.
When I mentioned domain in my first post. I did not mean the "domain name" I meant the whole website as a whole....
it would not affect at all since they are on different pages. Actually you can choose 1 to 3 keyword in a single site for effective seo. Keyword density is a must when optimizing single page.
keyword density is not considered site wise, only page wise, your initial example nameonthecake is wrong. The search engines love more pages, they understand that it's impossible (or very spammy) to write 10,000 pages about red shoes so they only consider keyword relevancy on a page scale, not site scale adding more pages will only help your rankings, even if they are different products, just don't go spammy