A　scheme　is　proposed　for　the　generation　of　superpositions　of　multi-mode　coherent　states,　i.e.　multi-mode　Schrödinger　cat　states.　In　the　scheme　a　A-type　three-level　atom　is　sent　through　many　cavities　filled　with　coherent　fields.　The　whole　system　is　entangled　via　the　Raman　atom-field　interaction.　Then　the　detection　of　the　atom　leaves　the　cavity　system　in　a　multi-mode　cat　state.　Under　certain　conditions,　such　a　cat　state　is　identical　to　a　Greenberger-Horne-Zeilinger　state　and　thus　can　be　used　to　test　local　realistic　theories.