While working on #19952, I needed quite some time to realize that the formulation in the original reference (http://www.gaussianprocess.org/gpml/chapters/RW.pdf) is not natively handling multioutput.

While it seems possible, we have very little information regarding this case. Indeed, there are several ways to handle the multi-output cases that I don't know anything about :)

However, I think that we should make sure that we are not supporting this use case badly. I think that we could have a look to https://papers.nips.cc/paper/2007/file/66368270ffd51418ec58bd793f2d9b1b-Paper.pdf