Multitasking TcpListener.AcceptSocket - multithreading

Question

In the code below, StartSocketListener has been started as a Thread. Sometimes, the processing of a message takes long enough that a couple of messages stack up (or at least that appears to be the case). I thought I'd take the socket and start another thread with it. I thought that passing the _HostConnection into the task would make concurrent instances of MessageFunction thread safe. Not so, it appears. I regularly get two kinds of errors: one is at _HostReader.ReadString, where I either read past the end of the stream or read only a portion of the stream (as if something else has consumed part of it). The other is at _HostWriter.Write, where I get "an established connection was aborted." Is it obvious where I've failed to get the thread safety that I was expecting? [I am a C# developer, so the VB lambda may look awkward :) ]
Private Sub StartSocketListener()
Dim _Listener As TcpListener = Nothing
Dim _HostConnection As Socket
Try
_Listener = New TcpListener(IPAddress.Parse(GetIPAddress), _TCPListenerPort)
_Listener.Start()
While _KeepListening
_HostConnection = _Listener.AcceptSocket
Dim MessageFunction = Sub(socket As Socket)
Dim _ClientIP As String = socket.RemoteEndPoint.ToString
Dim _HostSocketStream As NetworkStream = New NetworkStream(socket)
Dim _HostWriter As BinaryWriter = New BinaryWriter(_HostSocketStream)
Dim _HostReader As BinaryReader = New BinaryReader(_HostSocketStream)
Try
Dim _MsgXML As String = _HostReader.ReadString
If _MsgXML.Trim <> "" Then
If _KeepListening Then
Dim _RetXML As String = ProcessMessage(_MsgXML, _ClientIP)
Try
_HostWriter.Write(_RetXML)
Catch ex As Exception
...
End Try
End If
End If
Catch ex As Exception
...
End Try
_HostReader.Close()
_HostWriter.Close()
_HostSocketStream.Close()
socket.Close()
End Sub
Task.Factory.StartNew(Sub() MessageFunction(_HostConnection))
End While
_Listener.Stop()
Catch ex As Exception
....
End Try
End Sub