How this is done will determine if Google is OK with it and it's debatable because there is opportunity to get yourself into a pinch. To get to your primary question, yes, most likely, assuming you are covering some of the same keywords and industries, you will be competing against yourself for rankings (and possibly confuse your audience).
Multiple sites for one company or brand work best when there's better differentiation between them; for example, Honda has a site for cars and powersports, but a different one for financing. However, Ford pretty much rolls everything under one. So, again, the outcomes will be based on how you do it and what it means for the customer experience.
As for registration, we own a lot of domains and it's never been a problem.
While this is a direction I'd never advocate for, in your case, you don't mention why you want to go down this route, so I don't want to guess at your strategy and goals.
This article has some good details on risks especially in the comments ("Is Google OK with this?": http://www.seomoz.org/ugc/uncover-competitors-using-multiple-sites-for-multiple-first-page-rankings).