If you get an Italian visa, you don't have to apply for visas from other European countries, because Schengen countries are visa-free. Schengen countries are:
Austria, Belgium, Denmark, Finland, France, Germany, Iceland, Italy, Greece, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Hungary, Czech Republic, Slovakia, Slovenia, Poland, Estonia, Latvia, Lithuania, Malta, Switzerland, European Union and Liechtenstein. In other words, if you apply for any Schengen country, other countries can go.