How to log backtrace to a file instead of popping it up and blocking following backtraces

With emacs if there is a backtrace buffer open, new backtrace is ignored. I find it is unconvenient when I am trying to find out which function/hook changes a variable. I use debug-watch as described in Find out when a variable is changed in emacs - Stack Overflow The problem is the variable change happens after a backtrace buffer popup is impossible to know because of the backtrace blocking described above.

(debug-watch VARIABLE)

How can I make emacs popup as many backtrace buffers as possible or log the backtraces to a file?