I have some 10 to 15 pages that rank well for certain keywords. These pages receive consistent traffic from Google. These pages are about a year old. I want to update these pages with additional text and internal links. Will such an update hurt SERPs?
Search engine results pages (SERPs) and your rankings on them are a function of: your efforts, other websites, what interests the searchers (both what is searched for in a particular query and what was searched for previously, by you and others), and which search engine is used.
Location and the default language play a role also, if you search for Kale does the search engine think you mean a species of cabbage, a person's name or a place. That can depend on where you are, or if a movie is trending.
Will such an update hurt SERPs?
It is likely to alter them, in a few weeks. Done correctly you will improve your ranking, done incorrectly you will fall. The exact formula each search provider uses is tweaked to provide what they believe to be the best results. While each offers general guidelines, and there are plenty of webpages offering advice, the exact formula is guarded to prevent abuse.
Think from the viewpoint of the searcher, when they search for a particular subject what results would they prefer to receive. Pages offering value to the reader ought to index correctly for the particular term chosen. Pages simply offering a word match, and a bunch of ADs, ought to rank lower.
Additional text that expands upon the subject with internal links leading to additional relevant information is likely to improve your ranking.
Additional text that repeats existing information and links leading to subjects far removed from related searches ought to lower your ranking.