Claim before replying
Claiming signals that you are working on a ticket. Check the current owner immediately before a reply, especially on a busy live-chat queue.
Assign with context
Assign a ticket to the teammate best placed to act. Leave enough internal context in the thread for them to continue without asking the customer to repeat information.
Handle changes safely
If ownership changes while you are writing, pause and compare the newest thread state. Coordinate directly rather than sending two competing answers.