  We consider the problem of extracting tripartite entanglement through single
local instantaneous interactions of a separable target system A-B-C with a
scalar field. We find, non-perturbatively, that tripartite entanglement is
easily extracted in this scenario, in strong contrast to bipartite extraction,
which is not possible due to a no-go theorem. The tripartite entanglement is of
the GHZ-type, and an optimal value of the coupling exists that admits maximal
extraction.
