"Conversation Window" for @ replies

I just recently changed my settings to only show me @ replies directed at people I am following rather than all @ replies. This makes it a lot easier for me to keep up with what is important to me, however, there are times that I miss parts of a conversation because someone I am talking with gets a reply from another person and the conversation misses me.

I think a great solution to this would be a "conversation window" setting that you could configure to allow you to see all @ replies from a certain person for 5, 10, or 20 mins after you send an @ reply to them. Additionally, you could have it set to receive all the @ replies that are directed at that person as well.

So here's the concept:

I am talking to @personA and having a conversation. @personB is following @personA and hops in by sending a message to @personA related to what I am talking about and then @personA replies to @personB. If the setting is active and I made an @ reply to @personA within the time that my "conversation window" is set to then I would receive both the replies between @personA and @personB regardless of whether or not I am following @personB.

I think this would be an awesome feature that would allow people to focus more on the replies concerning them without missing replies related to their conversation.