make sure that search engines aren't indexing pages that wouldn't be useful to searchers (duplicates, poor content pages, internal site search results). Compare the amount of pages from the site's XML sitemap to the pages that have already been indexed by Google. Identify the URL parameters that the site has (via WMT) and see if those parameters are being indexed. Then just block access to them via robots.txt or by using the noindex tag.
Build more internal links to the site's key pages (product and category-level). If the site has a blog section, that'd be a perfect place to build more thematic internal links (to pass of authority/ranking ability to them).
Build incoming links to the site's important categories, so once you build up the authority of the site's categories, they can just flow the PageRank down to the product pages under them. And you'll have better chances of ranking for both short and long-tail search queries.
Start implementing structured data (schemas). They'll be very useful in the future.
Find 3 - 5 authority blogs in your client's space, and try to become a regular contributor/columnist (like submitting content twice or thrice a month). Creating signals through this approach (instead of guest blogging to hundreds of blogs) is definitely more efficient/realistic and a better combination with the continuous on-site changes that you'll be implementing on the site.
Use mention.net or fresh web explorer, and monitor where your competitors are getting mentions/links on a daily/weekly basis. That'll be a good head start in understanding your competitors' marketing activities (don't just copy them, beat them on their own game if possible).
Invest on relationships and strategic content partnerships. Invite guest bloggers or regular columnists for your client's blog, so you can also absorb their followers (your client's target customers).
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