So many times I've seen companies focus on links, only to end up frustrated. If you have a large number of links but your organic search is tanking, you may want to disavow all the "built links" that are obviously SEO-oriented.
Buying 10,000 links doesn't just get your low-value backlinks. It gets you penalized. In this article I tell a story of a company I worked with that had "built links" as an SEO strategy. They didn't even realize they had an algorithmic penguin penalty for 2 years of frustration because of the poor links.
We cleaned up, disavowed the links, and traffic started turning around. In this story, the graphs only show till October of 2014. The rest of the story is, by December, that company saw their business double month over month as a result of organic search.
Black/Grey hats will disagree with me, and they have methods that work in the short term. But for a company to build a real authority and organic real estate in their industry, you need to focus more on high-value content than link building.
I would use the panguin tool to see if there are any dropoffs in organic search results around the time of Google algorithm updates. If you see any, I would immediately start disavowing those trash links.
Then, I would invest in on-site SEO, making sure you are using best practices, not stuffing, etc. Make sure your on-site SEO is solid, and then start creating as much high-value content as possible, that is geared toward answering your customer's questions, the ones they ask before they buy.
This may be a TL:DR post, but I shudder every time I hear a legitimate company basing their strategy on "link building."