If the listing is still Incomplete, the co-list agent can access it and make changes to it, but will only be able to save it as INC. The co-list agent cannot switch places with the list agent and make themselves the primary list agent. Matrix will not allow this type of change to be saved.
Only the user who starts the listing (primary list agent) can save it as Active.
After the listing is changed from INC to Active, the co-list agent will also be able to access it for editing, as long as they are in the same organization as the list agent. If the co-list agent is in a different organization, only the primary list agent will be able to edit the listing.