We only offer ext4 filesystems on our linux droplets (aside from CoreOS which uses multiple partitions to do in place updates).
Is it possible to modify your partition table and add a new xfs partition?
There is no system in place to prevent this but we cannot provide any support for non-standard partitioning.
There are a few different ways to modify your partitions on a DO droplet that have been documented by third parties online. The easiest method may be to open a support ticket and request they mount the recovery ISO. This is a debian based LiveCD which will provide you with a CLI environment and the ability to use apt-get to install additional software. Using this you should be able to repartition your disk image. Once you are done, update your support ticket to have the recovery ISO removed.
Remember that since this is not a supported option, our support team will not be able to assist you with this aside from mounting the ISO and removing it when you're done. While our backup service should work properly even after you change your partition map I would recommend implementing your own backup solution as the backup system is not intended for xfs filesystems.