  We compute the N-jettiness soft function in hadronic collisions to
next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our
calculation is based on an extension of the SoftSERVE framework to soft
functions that involve an arbitrary number of lightlike Wilson lines. We
present numerical results for 1-jettiness and 2-jettiness, and illustrate that
our formalism carries over to a generic number of jets by calculating a few
benchmark points for 3-jettiness. We also perform a detailed analytic study of
the asymptotic behaviour of the soft-function coefficients at the edges of
phase space, when one of the jets becomes collinear to another jet or beam
direction, and comment on previous calculations of the N-jettiness soft
function.
