(This post uses the pronoun pattern subject/object/possessive/the other possessive/reflexive)
neopronouns are super useful for writing because they let you write gay without running into the issue of both people using the same pronouns. however, we do not have more explicitly-plural pronouns, making it hard to do the same thing with dynamics between groups, or hiveminds; and there may be any other number of reasons one might want to coin their own pronouns for a story.
When it comes to neopronoun coinings, if I want them to be perceived as loosely-masc or loosely-fem I tend to look at how the pronouns in consensus-english with such connotations are patterned-- "he/him/his/his/himself" and "she/her/her/hers/herself" respectively. Replacing with arbitrary sequences, we can get something like this:
he/him - A/B/C/C/Bself
she/her - A/B/B/Bs/Bself
A,B,C just denote arbitrary words, in a way that lets us see equivalencies between the different forms, and putting them next to "s" or "self" just denotes s/self is stuck next to them, in the order written. "they/them/their/theirs/themself" and "it/it/its/its/itself" can be analyzed with this paradigm as well, if one likes:
they/them - A/B/C/Cs/Bself
it/its - A/A/B/B/Aself or A/A/As/As/Aself (depending on interpretation)
Knowing these patterns can help us in coining new pronouns, particularly in our writing or if we want to be adjacent to, but not quite like, a certain more established genderfeel. (I would not recommend using this system to analyze existing neopronouns, by the way, as taking it too seriously might invalidate users of those neopronouns in many cases.)
I used this to coin a set of pronouns for myself, a "fem-leaning plural"-- lavve/lavre/lavre/lavres/lavreselves, which follows the she/her patterning. I'm not super happy with this set, and I haven't really been able to find a place to use it, but it's a good example of the sort of patterning I'm talking about and how you can use it as a template for your pronoun coinings.