Add sliced citrus, simple syrup, cinnamon sticks, cardamom pods, cloves, and allspice to the jar. Pour in vodka or grain alcohol to cover fruit completely. Shake gently. Store in a cool, dark place. Shake daily.
Pour contents through a mesh sieve into a bowl. Press fruit to extract liquid. Discard solids. Line sieve with coffee filters. Pour liqueur through filters into another bowl. Repeat if desired.