In a large bowl, combine heavy cream, Greek yogurt, and cream cheese (all well chilled). Add vanilla extract and maple syrup.
Using an electric mixer, beat on high speed for 4–5 minutes until thick, smooth, and creamy.
Pour milk into a shallow dish. Quickly dip graham crackers into the milk.
Arrange a layer of soaked crackers in a rectangular pan.
Spread one-third of the creamy mixture on top.
Add about two-thirds of the blueberries.
Repeat with another layer of soaked crackers and another layer of filling.
Slice two-thirds of the strawberries lengthwise and layer them on top.
Add a final layer of crackers and spread the remaining filling evenly.
Cover and refrigerate the No Bake Berry Ice Box Cake for 6–8 hours or overnight.
Before serving, decorate with remaining strawberries and blueberries.