Combine the flour, baking powder, baking soda, salt and allspice in a medium bowl. In a large bowl, beat the butter and sugars with a mixer at medium speed until fluffy, about 3 minutes. Beat in the eggs, one at a time, until well blended, then beat in the vanilla.
With the mixer at low speed, add the flour mixture in two batches, beating until just combined. Using a wooden spoon, stir in the oats, chocolate chips, coconut, pecans and dried fruit until incorporated. Cover the bowl with plastic wrap and chill for at least 30 minutes or overnight.
Position the racks in the upper and lower thirds of the oven and preheat the oven to 350 degrees F. Line baking sheets with parchment paper or silicone mats.
Drop the dough by tablespoons onto the lined baking sheets (you should fit about 12 cookies on each baking sheet).
Bake until the cookies are slightly browned around the edges and the centers are beginning to turn golden, 17 to 20 minutes. Let cool for about 5 minutes, then transfer the cookies with a spatula to a wire rack to cool completely.