I'm a citizen of Ukraine planning on visiting Italy early in October for tourism. Later that month I'm accepted as a speaker at the conference in Prague, Czech Republic. Both countries are members of Schengen agreement and a visa is required for me to visit them. Therefore, I need to visit Schengen countries 2 times and I need to get my visas ASAP (to confirm my talk to the conference organizers, as well as to avoid overpaying for hotels/flight tickets).
I've heard a number of times that a single person can't apply for a Schengen visa if already in possession of one, but I'd like to clarify this. Say, I've got a visa from Italy for the period of October 1st - October 14th. Can I get another one from Czech Republic for October 25th - October 30th before I visit Italy? Would the answer be different if I were to visit the second country (CZ) on October 13th - October 20th, thus, having a single day overlap between these visits. It would be of a tremendous help if you could link to the official documents that prove your point, but I'd certainly appreciate answers even without such links.
Both times I'm going to apply for a short-term tourist visa covering the dates of my travel. If the answer to both questions above is no - would several visits to multiple Schengen countries over a short period of time be a valid reason to apply for a single multiple-entry visa that covers the whole period from October 1st to October 30th from Italy?