Official band sites serve a lot of purposes many of which have to do with building relationships with fans, getting the word out about concerts and other crucial activities that have nothing to do with directly monetizing that exchange. It's important to keep that in mind when thinking about making more money from your official website.
Making More Money With Your Official Site or Blog
MonetizePros is a resource for learning how to make more money on the web. I previously referred to one of their free e-books when discussing how to make more money with YouTube.
I've mostly been following their blog where they share posts with such imposing titles as:
50 Blog and Content Monetization Strategies for 2014 & Beyond
It can be a bit much to take in but you'll find a selection of ideas and links out to services that can help you make more money with your website.
An Example: Affiliate Marketing Links
For example, the above post includes some tips on affiliate marketing, a topic discussed on Hypebot by both The Orchard's Tierney Stout and myself.
The most obvious way to use affiliate marketing on a website is to join iTunes' affiliate program so that when people buy your music on iTunes via links from your site, you get a percentage of the sale.
You can do the same with Amazon's affiliate program for physical CD sales.
Once you wrap your head around affiliate marketing for your own music, you can use it in other ways on your site. For instance, if you read a great book and talk about it on your blog, you can include a link to Amazon or another book site that has an affiliate program and benefit if readers buy the book after visiting your blog.
Other ideas won't fit. You'll see plenty of discussions regarding ad networks and, except in rare occasions, musicians shouldn't have ads on their sites.
Such distinctions are up to you but I think you can benefit from the range of possibilities discussed on sites like MonetizePros that allow you to develop a different perspective than one typically finds in the music industry.
Coming from web publishing, the affiliate concept is really obvious to me but I'm surprised at how rarely musicians employ it on their own sites.
Monetizing Your Social Media Presence
You can find out more about affiliate marketing and other concepts in the links above. I was actually inspired to post about MonetizePros due to their roundup of 442 Tips to Monetize Your Social Media Presence in 2014.
They include links to posts with tips on monetizing Facebook, Twitter, YouTube, Google Plus, LinkedIn, Pinterest and Instagram.
Brainstorm Freely, Then Apply With Care
It seems kind of nuts when you look at lists like this but take some time, put on your brainstorming goggles and consider the possibilities without censoring your thoughts.
Then, once you've got some new ideas, reconsider them in light of the particular channel you're planning to monetize, whether it's your official website or a social media account, and base your choices on how they fit what you conceive as the primary purpose for those channels.
So think freely and then apply with care. At the end of the day all your points of contact should support building better relationships and improving communication with your fans.