  We present a computation of the global soft function for single-inclusive
hadronic jet production at next-to-next-to-leading order (NNLO) in the strong
coupling constant involving four light-like Wilson lines. Our soft function
belongs to SCET$_{\text I}$ observables obeying the non-Abelian exponentiation
theorem. We provide the calculation of the soft function involving four
collinear light-cone directions for all $2\rightarrow2$ processes extending the
previous result. We perform the threshold resummation for these processes at
the next-to-next-to-leading logarithmic accuracy and present the corresponding
numerical results.
