So it looks like we already have the following factions already for a Wild Western Mars game:
BMT(BMT&EC), GMTC, AMTC - three competing trading companies
Earther 'law & order' - British and/or Japanese troops
Sky Martian infiltrators
Any number of Martian merchant houses/desert trader clans
Earther 'free traders'
Plus any number of new factions as our fevered imaginations think of new ones ...