I see the pragmatic maxim as a foundational insistence that all thought move toward some experimental process by which it can be validated. Thus in matters of religion, which can be described as supposition, the PM might place some weight on the experience Peirce describes in the NA (Neglected Argument). The implication being that the process of musement can lead to better expressions and behaviors.
Triadic Philosophy holds this point of view explicitly and argues that there is an inherent, positive result (reduction of possible harm) in conscious consideration of signs in terms of Reality Ethics and Aesthetics, using the ethical index of democracy, helpfulness, tolerance and non-idolatry and the aesthetic prod to truth-beauty, beauty-truth to create a positive expression or result.
The Neglected Argument of Peirce is not something I read before developing Triadic Philosophy.
Much of Triadic Philosophy is an amalgamation of about 10 years spent wrestling with Neitzsche (including a trip to Sils-Maria), decades of involvement with a critique of Christianity focusing on creedal messianism and experience in the world of mental health and with the thinking behind Roberto Assagioli's Psythosynthesis.
I saw Peirce as the generator of TP because his realistic premises seemed to me immensely relevant for now and the future. So I sit somewhat light to the text of NA and happily advance my own experience of using the elements of Triadic Philosophy to achieve results similar to those suggested by Peirce in NA and elsewhere.