Add heavy whipping cream, vanilla extract, and coconut extract to a medium-sized mixing bowl.
Mix until fluffy and able to hold stiff peaks (about 2-3 minutes). Set aside.
In a large bowl, cream the cream cheese until smooth.
Mix in powdered sugar gradually until combined.
Add the whipped cream to the cream cheese mixture by hand or with a mixer on low speed. (Be careful not to overmix, or the whipped cream will deflate) Cover and chill until ready to use.
Preheat oven to 350 F. Lightly grease the inside of 3 (9-inch) round cake pans with shortening and lightly dust with flour. Set aside.
In a medium mixing bowl, whisk flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream together butter, oil, and sugar.
Mix in egg whites one at a time.
Mix in vanilla extract, coconut extract, almond extract, and sour cream.
Mix dry ingredients with wet ingredients, alternating with the milk until all ingredients are combined.
Pour batter evenly into prepared pans (roughly 2 cups per pan).
Bake on the middle rack for 25 minutes. (May need a bit more or less time)
Let cakes cool in the pan for about 10 minutes. Carefully remove the cakes from the pan and place them on a cooling rack to cool completely.
Once the cakes are completely cooled, frost and stack the layers. Cover the top and sides with coconut.
Store in an airtight cake container in the fridge.