If you fit a 6870 RD and the firmware currently installed on your system is at the latest versions. The 6870 RD will not work at all unless you also buy a 6870 front derailleur. Shimano released a firmware update that prevents mixing a matching of 6770 and 6870 except the shifters.

If your firmware is still an older version, you can just plug in a 6870 RD and should work.

But installing a 6870 RD will convert your system to 11spd only. So you will need an 11spd cassette and 11spd chain. It will not work as 10spd.

Another option available to you instead of buying a new RD, is fitting a Wolf Tooth RoadLink
RoadLink ? wolftoothcomponents.com

It is a derailleur hanger extender that screws onto your hanger. And it will extend the current range of your short cage Di2 RD to work with a 32t cassette.