Sockets are thread unsafe at the stream level. You have to provide synchronization. The only warranty is that you won't get copies of the exact same bytes in different read invocations no matter concurrency.
But at a Reader and, specially, Writer level, you might have some locking problems.
Anyway, you can handle read and write operations with the Socket's streams as if they were completely independent objects (they are, the only thing they share is their lifecyle).
Once you have provided correct synchronization among reader threads on one hand, and writer threads on the other hand, any number of readers and writers will be okay. This means that, yes, you can read on one thread and write on another (in fact that's very frequent), and you don't have to stop reading while writing.
One last advice: all of the operations involving threads have associated timeout, make sure that you handle the timeouts correctly.
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