Well.... there IS an international-international transfer desk at PVG!
However - I have never once seen it staffed in the 15 or so arrivals I have made into PVG (at various times and days of the week) in the last year.
I also note that it only advertises very limited int-int transfers - I think VS, NZ and LH?? or something like that. Now that doesn't necessarily mean they don't handle other airlines...
However - given I have never seen it staffed I guess the easiest thing you can do is to use the transit visa-free option (if your passport is eligible) and just go out and pick up your bags and then head up one level and check-in again.
Check-in or the SQ flight should open 3 hours prior to departure, so by the time you have disembarked, done immigration, picked up the bags and gone upstairs you won't have long to wait (maybe 30 mins or so).
I remember seeing a similar thread to this on FT - might have been the China forum - but I can't remember if the answers were any more conclusive.