Preheat oven to 350 degrees. Grease and flour a 9X13-inch pan.
In a large bowl, combine flour, 2 cups sugar, salt, baking powder, baking soda, cinnamon, and allspice.
Add vegetable oil, vanilla extract, and eggs and stir just until dry ingredients are moistened.
Stir in banana, pecans, pineapple, and coconut just until evenly mixed.
Pour batter into prepared pan. Place in oven and bake for 40 to 45 minutes, or until wooden pick inserted in center comes out clean. Cool cake in pan.
To make Caramel Icing, beat cream cheese and butter until smooth. Beat in caramel-flavored ice cream topping and vanilla. Gradually beat in powdered sugar.
Spread icing on cooled cake. Store leftovers in refrigerator.