Settling before T+3?
It is possible but unlikely. Securities firms would prefer never to settle externally; rather, they prefer to wait until the liabilities can be netted.  They are forced to make and take payment in three business days. The reason why is because settlement is costly in the same way as any other business would prefer to build trade credit instead of taking or making payment rapidly. The only circumstance where a financial firm would wish to take full delivery is when a counterparty is no longer trusted to be solvent.