Google your DVD player's model number and see if there's fix (sometimes can be done from the handset).
May play on your computer -- if still a region problem Go Windows, Control Panel, System, Hardware Device Manager and the Properties of your computer's DVD drive and see if you can change the region code (be careful because they deliberately limit the number of changes allowed).
What error message do you get when you attempt to play R1 disk on multi-region DVD player ?
Maybe your DVD player is not region-free but simply a multi-region DVD player as you said. A multi-region DVD player may play DVD movie disks from several regions but not all. All DVD players are actually multi-region because they can play R0 and their own country region coded DVD disk.
You may get better luck trying videohelp.com or simply tell us your DVD player model- manufacturer. Maybe one of us can give you a helping hand.
VLC Player.. normally doesnt care what region your drive is... http://www.videolan.org/
"VLC media player
Does VLC support DVDs from all regions?
This mostly depends on your DVD drive. Testing it is usually the quickest way to find out. The problem is that a lot of newer drives are RPC2 drives these days. Some of these drives don't allow raw access to the drive untill the drive firmware has done a regioncheck. VLC uses libdvdcss and it needs raw access to the DVD drive to crack the encryption key. So with those drives it is impossible to circumvent the region protection. (This goes for all software. You will need to flash your drives firmware, but sometimes there is no alternate firmware available for your drive). On other RPC2 drives that do allow raw access, it might take VLC a long time to crack the key. So just pop the disc in your drive and try it out, while you get a coffee. RPC1 drives should 'always' work regardless of the regioncode. "