I would like to store a variable that is shared between all stack frames (top down) in a call chain. Much like ThreadLocal in Java or C#.
I have found https://github.com
Yes, it is possible. Thomas Watson has spoken about it at NodeConf Oslo 2016 in his Instrumenting Node.js in Production (alt.link).
It uses Node.js tracing - AsyncWrap (which should eventually become a well-established part of the public Node API). You can see an example in the open-source Opbeat Node agent or, perhaps even better, check out the talk slides and example code.