Any of O'Brien's works are relevant to this text. However, If I Die in a Combat Zone, which is actually mentioned in this text, makes a good companion to this text. Dispatches, by Michael Herr, is also a good Vietnam wartime text.
Consider also more recent collections of American war stories, such as Redeployment by Phil Klay.
In terms of structure, The Things They Carried is a collection of freestanding stories that are meant to be read together as one text. It is a novel in stories, so to speak. Consider other examples of this, like Naked Lunch, by William S. Burroughs.
