Concurrent MSc enrollment LSE and Bocconi in Italy?

I am a first year MSc student in Economics at Bocconi in Milan, Italy and I would like to apply for a 12 months MSc at LSE. My Italian MSc lasts 2 years, is it possible to apply and to be enrolled to the LSE MSc while I am also enrolled in my second year MSc in Italy. For Italian universities it is not a problem, what about for LSE?

Why would you want to be enrolled on two master's courses in different countries at the same time? How would you attend classes and tutorials?

What you can do (and perhaps you were meaning this) is apply to LSE while you're in your final year at Bocconi. As UK applications are always for the following academic year, this means that once you finish your course at Bocconi (presumably in the summer), you could start at LSE in the October of the same year.

Perhaps a broader question is why would one want to do a two year MSc Economics course at Bocconi and then another one year MSc Economics at LSE? Personally I can't figure out why anyone would want to do this. If you want to work after the MSc, Bocconi has a strong enough rep in London to provide you with good opportunities without the LSE master's. If you're wanting a stronger background for PhD applications, then working as an RA would be more beneficial (plus you get paid rather than having to pay LSE extortionate fees) than doing a second master's in the same field.