Articulating a template for the Five Ways might start by coining a term like “chain relative”
Chain relative: Whenever A exists relative to B, such that B itself can be considered as an A existing relative to B. Let a chain relation between a and b be aCRb.
Example: left is relative to right, but the thing on the right can itself be considered as something on the left of another thing. A son exists relative to a father, but that father can also be a son existing relative to a father, etc.
The paradigm for the Five Ways is thus:
1.) Some aCRb have a’s given to sensation. Among this subset:
2.) Some aCRb exist relative to b’s that are not a’s (b~a). Among this subset:
3.) Some b~a deserves the name God.
The chain relatives of the Five Ways are mobile and mover, what has an agent cause and agent cause, the contingent and the necessary, the more and less something to what is most (and these properties are themselves relative to degrees of being); and what has a goal without intelligence and what has goals with intelligence. The first two are easy to see, but the last three also appeal to chain relatives: the generated/ contingent reality of the Third Way relates to what is necessary, but this necessity itself divides into what is necessary by another (and so in some sense is contingent) and what is necessary by itself. The Fourth Way does not try to argue that God is the greatest good, but that things like goods have to be proportionate to beings, and God is the greatest among beings. The fifth way does not demand that everything that acts by intelligence is God (how could it?) but that, in effect, there must be something that acts entirely out of its intelligence without having to presuppose any given substructure of nature, subconscious drives, received ideas, etc.