Olives usually placed a distant second, except of course on fast days, and there were many. These were the liquids used to get fat into meals during fast days when animal protein and animal fat were forbidden. In regions where flavorful seed and nut oils were prevalent, they were used, especially the oils pressed from walnuts, hazelnuts, almonds. In many cases, one or more of these oils provided people with most of their fat calories both during the cooking and drizzled at the table.
Black truffle oil, argan oil, walnut oil, bergamot oil. If it ain't olive, it's in here.