Create a rule called Factions:

Each Settler has a Faction, which is publicly tracked as a string for that Settler and which defaults to Unaffiliated. The table in this rule lists all the valid values of the Factions field and their abbreviated names. When referring to a Faction, it is permissible to refer to it using its listed abbreviated name from the table.

All Factions have a list of Ostracised Settlers, defaulting to blank and which can contain any given Settler only once. Those Settlers may never have that Faction as their Faction. The Unaffiliated Faction can never have any Settlers listed as its Ostracised Settlers.

From the list of Factions, the Factions of Amber, Silver, Purple and Cobalt are said to be Kingdoms.

The list of Factions are:

{| class="wikitable"
|+ Factions
|-
! Name !! Abbreviated Name !!
|-
| Unaffiliated || Unaffiliated
|-
| Amber Archipeligo Autocracy || Amber
|-
| The Stratocratic Silver Steppe || Silver
|-
| The Purple Prairie Principality || Purple
|-
| The Cobalt Canyon Coalition || Cobalt
|-
| The Pirate League || Pirates
|-
|}

As a weekly action, a Settler can change their Faction so long as the following are true.
* The Settler is not changing their Faction from a Kingdom to a Kingdom, except if explicitly permitted by the ruleset.
* The Settler is not changing their Faction to one that lists them as an Ostracised Settler.

When they do so, if they are changing their Faction from a Kingdom, they must add themselves to that Kingdom’s Ostracised Settlers list if they are not already on that list. If they are changing to the Pirates Faction, they must add themselves to each Kingdom’s Ostracised Settlers list if they are not already on its list.

In the rule Working Together, replace its text with

For a Settler to have another Settler’s name in their alliance, the following must be true:
* Neither Settler may be on the other’s Faction’s Ostracised Settlers List.
* Either:
** The Settlers have the same non-Unaffiliated Faction.
** The Settlers have at least two numbers in common between their Domains. Only one matching pair of either 6 or 8 may be counted for this purposes.