Merge the threads first
Combine the messages into one ticket so every agent sees the whole story and nobody answers the same message twice.
Find out why they keep writing
Read the messages for the cause: no reply yet, an unclear answer, a deadline or a problem that is still happening.
Set expectations kindly
Say how long a fix takes and that you will write first when there is news, so they do not need to chase you.
Use the auto-reply carefully
If each email triggers an acknowledgement, the customer may feel processed by a machine. Turn it off for open tickets.
Escalate when it turns into abuse
Repeated contact is not abuse. Threats or insults are, and they follow your abuse process.