Cross Border Travel is generally allowed to:

Austria
Belgium
Denmark
Finland
France
Germany
Italy
Luxembourg
Netherlands
Norway
Portugal
Spain
Sweden
Switzerland
United Kingdom

and

Cross border travel is generally not allowed to:

Albania
Belarus
Croatia
Czech Republic
Finland
Hungary
Poland
Slovak Republic
Russia
Estonia
Lithuania
Ukraine
Moldova
Romania
Bulgaria
Greece
Turkey
Asia
Serbia
Bosnia
Montenegro
Macedonia
Kosovo

Hertz was a little bit different with regards to cross border travel into Croatia:

Hertz vehicles cannot be driven into and/or dropped off in any African, Asian, or Middle-East countries, nor in Albania, Armenia, Azerbaijan, Belarus, Bosnia-Herzegovina, Bulgaria, Czech Republic, Estonia, Georgia, Greece, Hungary, Kazakhstan, Kyrgyzstan, Latvia, Lithuania, Macedonia, Malta, Moldova, Montenegro, Poland, Romania, Russia, Serbia, Slovakia, Tajikistan, Turkey, Turkmenistan, Ukraine, Uzbekistan.

Hertz vehicles MAY be driven into Slovenia and/or Croatia but you need to inform the pick-up location in order to get the authorization that needs to be presented to the customs authorities.

I did find a car rental company called Kemwel(kemwel.com) and while searching through their cross border driving policies from rentals in Italy I found:

General Information

Many of the vehicles rented through Kemwel in Italy can travel throughout Western Europe without any restrictions. There are some vehicles; due to insurance regulations that may not be able to travel into certain countries some of the vehicles include luxury vehicles, automatic vehicles and vans.

Due to Kemwel’s great relationship with its suppliers, it has allowed for the creation of a special program that will allow for travel into select Eastern European countries.

An additional surcharge may apply for rental vehicles being taken into Eastern Europe. When planning your itinerary please take into consideration if it will be possible with the category of car you are planning to rent.

Restricted Countries

Vehicles rented in Italy through Kemwel cannot travel into or through the following countries without prior notification and approval from Kemwel and our suppliers: Albania, Bosnia, Belarus, Bulgaria, Czech Republic, Croatia, Estonia, Greece, Hungary, Latvia, Lithuania, Macedonia, Moldova, Montenegro, Poland, Romania, Russia, Serbia, Slovenia, Slovakia, Turkey and the Ukraine.

NOTE: Travel into most or all of these countries can be arranged for specific car categories with advance notice to Kemwel additional fees may apply.