I have an imported object with 2 .png textures. Under material>settings I can adjust the clip threshold and one texture will gradually appear over the other. If I duplicate the object, I cannot do the same for duplicates unless I turn on backface culling or go into the shader editor and change the Alpha from Straight to Premultiplied, and even then that only works once. My goal is to be able to duplicate the object with duplicates of the .png textures and be able to adjust the clip threshold independently of the others. What am I doing wrong?
Alpha clip is a material setting, not an object setting. Any time you change it, you're going to be changing it on all objects that have that material (and, you're only going to be changing it for those faces assigned to that material.)
By default, Blender leaves materials linked when you duplicate objects. You can tell it that you want it to unlink these materials on duplication in preferences, in the editing tab, by enabling duplicate data/material. Once you do this, every object you duplicate will have its own copy of the material, and so changing the alpha clip on one will have no effect on any of the others.