  In this work we deal with the recently introduced concept of weaving frames.
We extend the concept to include multi-window frames and present the first
sufficient criteria for a family of multi-window Gabor frames to be woven. We
give a Hilbert space norm criterion and a pointwise criterion in phase space.
The key ingredient are localization operators in phase space and we give
examples of woven multi-window Gabor frames consisting of Hermite functions.
