Yes, it’s possible, provided that you are sending multiple parcels to the same recipient/address.
The driver will only pick up all packages if the order is registered on his PDA (Personal Digital Assistant or handheld computer). For this reason, he will only take the scheduled parcels to collect on that day.
If you hand over the goods to the driver at an anticipated date the traceability could be lost (loss risk ) and/or the goods could be accidentally crossed (especially in international shipments re-labeled by the carriers).
Also, please note that even if you have handed over the package earlier, the transit time will be counted from the initially arranged collection date since the carrier will not have the order in the system to be able to start the transit.
So even if the driver accepts, do not hand over the goods before the scheduled collection date.