I will describe a connection between multiple polylogarithms on tori and the Steinberg module of rationals, and show how this connection can be used to prove that all multiple polylogarithms of a given weight 
and depth can be expressed via a single function. If time permits, I will also discuss how the story relates to stability questions for cohomology of GL_n(Z). The talk is based on a recent joint work with 
Steven Charlton and Daniil Rudenko.