Allspice is a dried fruit from Mexico and Central America. Pumpkin spice has a more robust flavor and allspice enhances that flavor. Yes, you can and I often use this mix for that very reason.

In the following decades, the now-named spice mix became a staple on the shelves ... believe pumpkin to be native to North and Central America. Now, the term pumpkin spice, or pumpkin pie spice ...