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I am a Chinese student in the UK. I just got my Schengen visa from Norway. They only gave me a single-entry visa, from 3rd July to 25th July, and I can only stay in there for 8 days. I will be in Norway from 3rd July to 10th July, that's fine.
However I need to travel to Italy on 18th July, and back to the UK on 23th July. Can I apply for a new Schengen visa for Italy in a situation like this?