Preheat the oven to 350° and position 2 racks in the lower third. In a medium bowl, whisk together the flour, baking powder, baking soda and salt. In a large bowl, using an electric mixer, beat the butter, brown sugar and granulated sugar until fluffy. Beat in the eggs and vanilla at medium speed until combined. Add the dry ingredients and beat at low speed until barely combined. Add the coconut, chocolate chips, raisins and nuts and beat until they're evenly distributed.
For each cookie, use an ice cream scoop or a large spoon to scoop 3 tablespoons of the dough onto parchment-lined or nonstick baking sheets; space them 2 inches apart. Bake the cookies for 15 minutes, until lightly browned and crisp around the edges but a little soft in the center; shift the pans from top to bottom and front to back for even baking. Let the cookies cool for 10 minutes on the baking sheets, then transfer them to a wire rack to cool completely.
The cookies can be stored in an airtight container for up to 1 week.