The Carrier Item only services one of the Objects that want it
Q: My Carrier Item only services one of the objects that wants it. This assumes the Carrier Item is waiting in a Dispatcher which has multiple outgoing paths to many PickUp Objects.
A: The Dispatcher Object holding the Carrier Item has an implicit ordering of the outgoing paths it seeks to use.
Whenever Objects are in competition for the services of the Carrier Item, it chooses the first outgoing path (in the order of path number).
Instead of laying many paths out of the Dispatcher, connect a single outgoing path from the Dispatcher to a Switch that you have configured to assist with the decision making. Branch the Carrier Item's paths from there and you should be able to create the kind of prioritisation or balancing you need.