It seems there are many itineraries that depart from Barcelona or Southampton that don't go east of Venice - though you are really missing out if you don't.
Also, Costa has routes that navigate around Italy if that is your focus.
A Bad Day At Sea [with power] Always Beats A Good Day At Work
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014