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Doggit
It's the other end of the landing that sits on the wall you want to remove, so you'd need to run an RSJ or beam across to the other side of the kitchen to replace the support. Although if you didn't mind the odd look, you might be able to run a shorter one from the stairs/kitchen wall, under the corner of the landing, and then to the outside wall. You could then box it all in to make it look neat, and have a few downlighters for the kitchen table.