By multi-output GP do you mean high dimension observation or repeat observation of the same GP?
For high dimension problem you just need to specify the dimension in your Mean and Cov function.
For repeat observation of the same GP @jordan-melendez gives quite a good solution in another post: Multiple (uncertain) function observations of the same Gaussian process
I think the additional features you need is also possible even with the current API, you just need to carefully structure and parameterize your Cov function.