Can I use the supernant of the transfected packaging cells to re-infect the packaging cells and get higher titer virus?
No. The reason why re-infecting the transfected cells does not lead to higher titer is because our lentiviral vectors are SIN vectors. Following infection and reverse transcription, the deletion in the U3 region gets copied into the 5'LTR resulting in little if any transcription from the LTR. Transcription from the 5'LTR is what generates the viral RNA that gets packaged into the lentiviral particles.