Outherine Flag
Outherity (outherinity/outhrinity/outhrity): a descriptor of new gender qualities (attributes or essences), to give a general name for a fifth, sixth, seventh, etc. quality.
Folks can describe outhrine/outherly qualities can as apart from those other four ones (neu/masc/angi/fem), yet not exactly xenine; entirely new but can be compared to the overall four terms; or unique combinations among the otherly four (i.e. simultaneously neutral & masculine yet seeing it as something different or separated).
May even be useful for people with culture-exclusive genders, if they think the overall four qualities do not apply to their identities and/or experiences.
Similar to aporaine/aporine and nonquad(ri)nary/nonquaternary. Not to be confused with otherkinity. Coined by @oltiel