Stop. Now. Before you shoot your client (and yourself) in the foot.
The domain name does not carry the SEO weight you seem to think it does. You might want to check this to learn more about factors that weigh more heavily, and what the 35 recognized search industry experts surveyed think about the value of a so-called "keyword rich domain" (and the reasons for whatever value it might have):
Bottom line, it is almost certainly not
the lack of keywords in the domain name that's making it hard to rank for more competitive terms.
Company names are almost by definition brandable. "Brand" doesn't have anything to do with keywords. In fact, generic "keyword" phrases are pretty much the opposite
of brandable, because instead of being unique to the company in question (like the company's name) they can be used by anybody.
Think about the big brands. Does the word "Exxon" say anything about oil refining or gasoline? Do the words "Target" and "Wal Mart" in and of themselves say anything about discount retailing? What does the word "Amazon" have to do with books or online selling? And yet, when you hear these non-keyword-words, it's likely the first thing you think of is the company in question, and what it does. That
There's nothing stopping you from optimizing for words and phrases other than the company name, using other factors that carry much
more weight than the domain name (page title tag, on page text, anchor text of links pointing to the page, etc.) More competitive keywords are going to be harder to optimize for -- for the most competitive, you will have to get more factors right and put in a lot more work. Nature of the beast.
But having keywords in the domain is not some sort of magical silver bullet. In fact, because it means you're effectively saying every page of the site is about the same few keywords, you could be making your job harder in the long run. Each page should be optimized for 2-3 key phrases, different phrases for each page. If you want to get key phrases into your URLs, use your folder and file names to do so, not the domain, so you can target different keywords on each page.
(Keep in mind, if you change the file or folder names of existing pages, you need to 301 redirect the old page URLs to the new ones to avoid broken links and to keep the SEs from getting confused.)
A big problem with keyword-focused domains is that they don't age well. Keep in mind, what the company makes/sells now may not be what they're making/selling in the future. And even if they continue to sell the same products, the market can change. The words and phrases customers use to search for those products today may not be the words and phrases they use tomorrow.
You simply cannot run around changing the domain name every time the company changes their product mix or their customers change their minds. Down that road lies insanity.
Because when you change the domain name, you will
incur issues with the search engines. Yes, you can use 301 redirects to make sure visitors reach the new pages and to (eventually) transfer link juice from the old domain to the new.
But it will take time for the SEs to sort out the changes, and in the meantime, the site will
take a hit in rankings and traffic. And there's no guarantee the rankings will fully recover after the change. (No guarantee they won't, either, of course, but why take a chance if you don't have to?)
If you have a well-performing site that's got a bit of age on it and a modicum of links pointing to it, IMHO you'd be nuts to change it just because of some misguided notion of having a "keyword-rich" domain. Optimize the pages you have; create new pages to optimize them for additional phrases; use your site navigation to spread the link love around to all these pages.
I promise you by effectively optimizing the site they already have, you will do as well (or better) than you'd do by embarking on an ill-advised scheme for moving them to another domain.