I belive Exiv2 can read and write custom tags. Exiv2/XMP support is a wrapper over the Adobe XMPsdk. I know for certain you can add your own namespace (in addition to almost 60 which are predefined). There would be no point in adding a namespace if you could not define your own tag! So, I’m 99+% confident that you can define your own tag.
Exiv2 enables you to read/delete/add/modify most tags in Exif, IPTC and XMP format. There are a few protected tags which are part of the image. For example, although the image width and height (in pixels) is metadata, it cannot be modified by Exiv2 as it would involve scaling/resampling the image. There are many other libraries which provide such pixel twiddling capability.