Once this checkbox is marked the link will always set:
the earliest possible Start Date of the linked target task if Start Date is the target
the earliest possible End Date of the linked target task if End Date is the target.
In other words - link in ASAP mode always schedules target task as soon as possible based on dependency type. There are no restrictions on how many links are created for each source or target task as long as they are not creating a circular relationship (discussed here). If a task is moved to a prohibited position (based on link type and mode) it is moved back/forward to the appropriate position.