In the bowl of a stand mixer or in a large bowl using a hand mixer, beat cream cheese, both sugars, and ½ cup caramel until fluffy and combined. Add heavy cream and beat until medium peaks form.
Add mixture to pie crust and smooth top. Refrigerate pie until firm, 6 hours.
Spread remaining ½ cup caramel on top of chilled pie, then top with coconut mixture, pressing down to make an even layer.
Lightly drizzle with more caramel and melted chocolate and serve.
