Can I add more than one "h1" tag without damaging the main header?
That kind of depends on how they're being used now. I assume, if you have a unique, well-conceived <h1> heading for each page, that adding <h2> elements would be a better way to go.
For a long discussion on the topic, one of a great many.... Two H1 tags on One Page - Effect in Google SERP http://www.webmasterworld.com/google/3773892.htm
The <h1> is not a magic bullet and some recent tests have shown that, at least by itself, the <h1> doesn't appear to affect rankings in Google.
I feel, though, that using an <h1> as a structural element in a well-structured page is beneficial... but that may have more to do with the effects of discipline applied to the creation of a good page structure than to the weight currently assigned to the <h1> by Google.
I continue to use the <h1>, along with <h2>s, <h3>s, etc, in a well-structured page format. If I'm called to optimize a site and I see that the designer has, say, reserved <h1>s for formatting testimonials, or has applied <h1>s blindly to the first piece of text on a page (no matter what that text is), I take that as another bit of evidence that the pages probably haven't been well structured, and I do my best to fix page structure and content when I fix all the rest.
Two <h1>s on a page, at least for now, are often a sign that something hasn't been thought through. There's been so much misuse of <hn> elements by would-be SEOs that the engines have evolved (out of necessity) to where they see beyond the labels we put on pieces of text. I'd recommend taking that approach too and looking at how your pages are structured overall. At the least, though, the heading levels are still a very helpful tool. You might want to think of them as outline levels.
HTML5 will allow multiple <section> elements, and within each <section> element an <h1> will be appropriate. As I understand it, and at this point my understanding of HTML5 is incomplete, a <section> element won't really be appropriate unless it contains a main heading that sets it apart... ie, it's not the same as a <div>.
HTML5 structuring is down the road a bit. It will require more structural discipline, not less, than current HTML4 structures suggest. It's hard to say how HTML5 will affect SEO.