In the rule “Possessions”, add the following text:

Each Thief has a Transfer, which is privately tracked by the City, defaults to empty, and is either empty, or contains a list of one or more of that Thief’s Possessions and a Thief who is the Destination of that Transfer. A Thief may set their Transfer by privately communicating the desired value to the City.

In the subrule “Distribution”, after the first step of the atomic action “Distributing It” add this step:

* For each Thief who has a non-empty Transfer, remove the Possessions listed in that Transfer from that Thief, skipping any that are not actually in that Thief’s inventory, set that Thief’s Transfer to empty, and add the removed Possessions to the inventory of the Thief named as the Destination. Privately communicate to the Thief named as the Destination the value of each Pouch in the Transfer using the name of each Pouch.