How to structure a statement will not only depend on the goal of the statement itself, but also on the body of text which surrounds it. In all cases, you must indicate who “they” or “them” are, either in this statement or another. Since this, I assume you are referring to a group of individuals, such must be identified in close proximity.

For my direct answer, “them’s”, “each’s,” is not possessive form. Now what is the meaning of each of these words?

What are the objections

to each individual?

What

are the objections? How individual was defined in the preceding text. From each individual

being a person. (Depending on his/her individuality.)