In Battle-Mode can any unit within a faction use any items/mods within that faction?

In the Faction force lists there are multiple sub-factions, can you use any weapons/items from any of these sub-factions so long as you are in the “Main” faction?

example, can Elder Maxson from “MAXON BROTHERHOOD OF STEEL” use a item/weapon from “LIONS BROTHERHOOD OF STEEL” list?

I already assumed we cannot use items/weapons from other main factions and also that you cannot mix units from different factions on the same team.

These item’s lists created to use only their own weapons. So by default you cannot use Lion’s weapon in Maxon`s sub-faction.
But you can use home rules if you wish.