  On-shell recursion relation has been recognized as a powerful tool for
calculating tree level amplitudes in quantum field theory, but it doesn't work
well when the residue of the deformed amplitude $\hat{A}(z)$ doesn't vanish at
infinity of $z$. However, in such situation, we still can get the right
amplitude by computing the boundary contribution explicitly. In
arXiv:0801.2385, background field method was first used to analyze the boundary
behaviors of amplitudes with two deformed external lines in different theories.
The same method has also been generalized to calculate the explicit boundary
operators of some amplitudes with BCFW-like deformation in arXiv:1507.00463. In
this paper, we will take a step further to generalize the method into the case
of multiple-line deformation, and to show how the boundary behaviors (even the
boundary contributions) can be extracted in the method.
