It would take a lot of money and a lot of time but it is do able. If you do a yahoo site explorer search for back links on the domain you want to bump off it's very likely you will find find hundreds or even thousands of backlinks to that domain (if you are going after something like PCs or Cameras)so you would need to get more backlinks and equally as good on page optimization if you want to out rank them.

Your other alternative would be PPC marketing, but depending on the terms of the company (if you can even use their name in your marketing) and the cost per click (CPC) this could cost you a great deal of money as well. (possibly upwords of $1 a click)

So, yes it is possible to do it the SEO route with enough time and energy spent, but we are talking a couple years here. If you are trying to make money NOW you would be better of to target a smaller niche or maybe even one particular product and try to dominate that way.