It may help for Venetian Republic to completely knockout the local rivals, such as Genoa, Amalfi, Pisa, and prevent the rise of the Duchy of Milan. With much of the city-states and duchies of Italy subjugated, Venice may be able to punch well above its weight in terms of long-range military ventures. Also, securing some of the important ports of southern Spain and Morrocco sometime between th 1200-1300's, and preventing any unification of the Iberian states would strenghen Venice's capabilities in the Western Med.
Oh yes, and the rise of the Ottoman Empire may need to be curtailed as well. Due to its geographic position and demographic scope, Venice's competition within Italy and the Mediterranean would need to be fairly limited before it could extend its reach anywhere else.