Prepare the popcorn. Place 12 cups of popped popcorn in an extra-large bowl. Carefully remove any unpopped kernels and set the bowl aside.
Make the marshmallow coating. Combine the corn syrup, butter, powdered sugar and marshmallows in a large saucepan. Cook over medium heat, stirring frequently, until the marshmallows have melted and the mixture is smooth and just beginning to bubble.
Coat the popcorn. Carefully pour the hot marshmallow mixture over the popcorn. Stir gently with a wooden spoon or sturdy spatula until the popcorn is evenly coated.
Add the candy. Immediately fold in the candy pieces, if using, while the mixture is still warm and workable. Some chocolate candy may soften or create streaks throughout the popcorn.
Let it cool briefly. Allow the coated popcorn to cool just until it is safe to handle. The marshmallow mixture will be very hot when it first leaves the saucepan, so an adult should handle the cooking, pouring and initial stirring.
Shape the popcorn balls. Coat your hands with nonstick cooking spray. Scoop out approximately 1 cup of the mixture at a time and gently press it into a 3- to 4-inch ball.
Let them set. Place each popcorn ball on wax paper or parchment paper to cool completely. If the balls begin to loosen, gently press them back into shape before the coating sets.
Wrap and store. Once completely cool, wrap each popcorn ball tightly in plastic wrap. Store at room temperature for up to seven days.