If you want your content to spread farther, make it reflect well on the users you're depending on to carry it to wider audiences.
Social media is personal - that's what distinguishes it from public media. This is my news; these are my friends; these are the jokes that I find hilarious. The things we choose to share through social media reflect personal interests and attitudes, whether we're illustrating what we agree with or what we find deeply repellant. This is a conscious choice in many cases, but not always. Research shows that Facebook 'Likes' are shockingly accurate predictors of a wide array of attributes, from intelligence to sexuality.
With this in mind, it's easy to see why the updates and articles your accounting firm posts on social media channels speak to certain of your followers. To some extent this is as obvious as anything could be. Your friends and followers are by definition composed of a self-selected group who have an interest in the topics and services you focus on. You should expect that a good portion of what you share will resonate with this group simply because they've already indicated their affinity for you and your ideas, as well as a general interest in the area you represent.
Good content should have an appeal that's close to universal. That is, it should be written clearly and in a style that easily conveys its message to the broadest range of readers possible. There are subgroups within your followers whose needs and life situations will create a greater or lesser level of interest for any particular post, but anything you post should have a good chance of appealing to many of your readers and others like them. So what makes the difference between sharing and simply reading?
The answer lies in the personal nature of social media. Since sharing is about personal branding, just as it is about firm branding, you must align your posts so closely to your readers' identities that they perceive the choice to share your content as one that furthers their personal brands. After all, there are going to be many posts that discuss the same information. Readers with an interest in the topic can find plenty of options. Choosing yours as the one to share is based on not only the information it contains but the voice it uses, the attitude it implies and the style it shows.
Your firm's posts may be appreciated by many who read them, but spreading farther than your original audience will come from hitting just the right note. Whether original content, or even commentary you have on another article, the decision to share it in their own accounts is driven by your readers' willingness to identify with it as something they wish they'd said themselves.
To maximize sharing, therefore, you need to understand who your readers are, how they see themselves and how they'd like to be seen. Study the metrics about your firm's content: which pages are most popular and which content gets the most attention? But also do what you can to really analyze your best clients. Who are they? What is it about you that makes them loyal? That's your answer. Your unique attributes and style reflect their desires and self-images. Speak to those points effectively in your content and you'll find your readers more than willing to share it, not only for its intrinsic use value but also for its ability to build their personal brands.