Is there a way to disable the feature where if someone answers a chat thread in a Team, it pushes the entire thread to the bottom of the page? We have some fast paced support teams where a lot of questions are being asked, but questions get missed because older threads get pushed to the bottom of the page. 

AFAIK, there is not a setting to configure this apart from pinning chats in the chat area. By the way, chats should not be pushed back immediately to the bottom of the chat area...the way it works is that you always see recent chats at the top of the chat area (just behind the pinned chats)
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