It is not obvious what benefit the search for additional debris might bring.
Wreckage does not help clarify the cause or the location of the accident, just the nature of the final ditching.
Airlandseaman argues convincingly and with factual evidence that the aircraft went down without pilot intervention, a Helios like flight into nowhere, with a high speed crash at the end.
To perhaps find out what brought that about the authorities would need to find the CVR and FDR. Unfortunately, assuming the simulation is reasonably valid, the wreckage is unlikely to include any large pieces. That lengthens the odds against finding the crash site.