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Well, you could try it, but a page can only have one title. Your web browser will pick the last one, and we don't really know what Google will do.
It sounds like you're going about this the wrong way. You don't just throw tags around keywords you want to the search engines to rank you for; the Hx and title tags all have visual properties, and when you need a particular one to get that effect is when you use it. Design your pages for the people who will read them, not the search engines.
The header tags put the text inside them on its own line, as if there was a <br /> tag before and after them. Which makes them great for actual headlines, but will break a paragraph if you try to <h2> a keyword. The idea is to briefly describe what the paragraphs that come next are about in a heading, so a user can scan your page quickly and decide what to read. Because of all that, Google gives extra weight to text in Hx tags.
What it sounds like you're trying to do, optimize for a few particular keywords in your text, is usually accomplished in two basic ways: on-page optimization ( what you're doing ) would mean including a keyword or two in your title, having an h1, some h2s, and so on, that might have a keyword in them. Not the same as in your title, mind you. The second is off-page optimization, where you collect links pointing back to your site with your keywords as anchor text. ( Think: <a href="#">anchor text</a> )
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