I don’t recall an additional setting for auxiliary copies which results in what you are describing.
You would be better of editing the auxiliary copy schedule and use the option “Continuous” with a certain interval in minutes. This way an auxiliary copy needs to finish before another can start.
In regards of backups this can be partially achieved with an additional setting called:
JMDontStartBkpsIfConflictingJobRunning
https://documentation.commvault.com/additionalsetting/details?name=%22JMDontStartBkpsIfConflictingJobRunning%22&id=12684
This will start the job, but when it fails due to a conflicting job it will not register in the job history.
But again you would be better of editing the schedule and selecting the “Continuous” option, assuming your backup window will allow for deferred scheduling.
Hope this helps.