How to approach SEO for a large site that doesn't have specific keyword goals?

[jpea]

So, I have a project that has 10,000+ page of unique editorial content in a specific industry. They currently get about 500,000 pageviews a month and average just under 2 pages per visit. It has a 66 domain authority and has been doing "the basics" for SEO for about 7 years (headline is an H1, URL is custom while the headline is more "reader friendly", description is a snippet of the body copy a little into the first paragraph, nofollow in the comments).

The crux is that it's an editorial publication so they're not targeting specific keywords, but a wide swath of keywords.

Would it be best to just dive in and figure out some of the less competitive keywords for some of the articles that they could tailor some content to rank better for, then just move onto more and more? What are some ways to approach this if they just want to raise their general traffic and relevancy to the next level?

[jpea]

Thanks Theo!

I'll try to go in order here:
1 - Not selling anything, but serving ads. It has a small affiliate shopping functionality that is hard coded into the HTML, but with a max of 3 links on a page for those. 
2 - Search=43%, Direct=25%, Referral=32%
3 - Visitor interaction are comments or social shares. 
4 - I'm somewhat of a noob, so I don't really know what to call a conversion here? 
5 - The IA seems to be pretty good overall. There are categories in the top nav, the content is easily readable and at a good text size, a fairly common site overall structure and aesethic-wise. Is it appropriate to mention the site in question here? It's not a traditional "client" of mine so they're open to any help.

[EGOL]

Search=43%, Direct=25%, Referral=32%

This site has a tribe of people.

So, it must have some content that is highly appealing to some people.  I would break out the analytics to see what type of content is being referred and direct... and what is from search.

I would be sure that I made this content very easy to share.

Does this site have a feed that people can subscribe to?  I use feedburner on one of my sites and have about 20,000 subscribers.  When I post something new it gets immediate action.  This site could do the same thing.

[jpea]

Wow, thanks for the thorough replies!

EGOL:
They're definitely open to content direction. I'm wondering if the tweaking of existing low-ranking content would be worth it (will it get indexed again even? will raising the ranking of low-competition and low-traffic content help as much as new content with new direction in mind?)

[EGOL]

Right....  I have a site that gets low monthly traffic per page.  The way for me to get more traffic is to get more pages up.   Since it is in a low competition niche the new pages immediately rank really well - so I don't have to worry much about increasing my power.  Instead I focus on getting keyword reach with more pages.

[Vizergy]

"If I was the owner of that site I would want information on what type of content is bringing in the visitors and what kind of content isn't.  Then, using the successful content as a guide I would try to produce more of that kind of stuff."

Completely agree.  On any site the content is the most important but on a website like this it is almost everything.

[EGOL]

This site seems to be successful if it is generating 500,000 pageviews per month....   however, that really boils down to an average of just 50 pageviews per month for the average page.

So, in my mind, some of their content is successful and some of it isn't.

If I was the owner of that site I would want information on what type of content is bringing in the visitors and what kind of content isn't.  Then, using the successful content as a guide I would try to produce more of that kind of stuff.

Also, where is this content coming from.  Search?  Return visitors?  Does this site have a feed that has a big tribe of subscribers who account for most of the pageviews.  If most of the pageviews are coming from the tribe then a plan to enlarge the tribe or get then to evangelize might yield great results.

I would also look at the content that is not bringing in much traffic from search.  Why not?   Are the title tags clever instead of keyword targeted?  What can be done about that?

There are lots of questions when you have a site like this.  Some of the answers will yield payback and some will not.

[Theo-NL]

That will mainly depend on their goals. Are they trying to sell anything (services, products?) or perhaps show ads? Depending on these goals you for example could try to find ways to increase pages/visit or the number of visits. If they are scoring well on the long tail (which it seems they are) you might want to increase the visits from short tail keywords. How is the split between search/direct/referral, and if skewed, what can you do to change this? Is there any visitor interaction, and if not, is this desired? How are the conversions on the website? Is there any related content that draws visitors deeper into the website? Is the information architecture set up in a way to maximize the (apparently valuable) content to visitors?