Insert or include something extra, as in Can you run this map in with the text? [Early 1800s]
Also, run on. In printing, make a solid body of text without a paragraph or other break, as in The quotation should be run in rather than set as a paragraph.
Also, run someone in. Take someone into custody, as in The police were going to run him in, but he got away. [Slang; mid-1800s]
Visit someone briefly, as in If I have time, I'll run in to see Aunt Mary. [Second half of 1800s]
Break something or someone in, as in Let's run in the new model on a short flight. [Early 1900s] Also see run into.