Add the Crispix to a large bowl with a lid; set aside.
Place the powdered sugar and 16 of the Oreos into a food processor. Pulse until you have a fine powder; set aside.
In a microwave-safe bowl, combine 2 cups of the white chocolate chips, the semi-sweet chocolate chips and the peanut butter. Microwave, stirring every 30 seconds, until melted and smooth.
Pour the chocolate and peanut butter mixture over the Crispix cereal and gently stir to coat. Continue until the cereal (even the stuff at the bottom of the bowl!) is evenly coated.
Dump the powdered sugar and Oreo crumb mixture over the coated cereal. Place the lid on the bowl and shake to cover the cereal in powder.
Remove the lid and let the puppy chow cool completely.
Next, coarsely chop the remaining Oreos. Add the Oreos and remaining white chocolate chips to the puppy chow and stir until they're scattered evenly throughout.
Store in a tightly sealed container or resealable baggie at room temperature, in the fridge or in the freezer.