1. language features we have and they don't understand
2. language features we both have
3. language features they have and we don't understand
Probably in that order.
Then it's just a question of gathering a couple of different species that are seemingly intelligent. Such as: corvids, octopuses, whales, etc. And see if the species can be reasoned with. If so, then you can set up schools where you can train them on human things and vice versa. Eventually you can form interspecies groups and really test the hell out of things.
Doing it that way will really challenge human exceptionalism, as well as the exceptionalism of that particular species.
I know it sounds a bit far off, but I figured that we might be able to get there with AI. I mean, we're getting better and better at giving machines tons and tons of data, and it somehow makes some sense of it.
So far, I think it's not necessarily the human species that is exceptional. It's the revolutionary periods it went through in order to become more exceptional hunters, so we could dominate and control the world in the way we want to. Things such as: discovery of fire, agriculture (+ creating defensive settlements) and antibiotics. We couldn't kill bacteria for a long time. We still have trouble with viruses and are getting into trouble with bacteria again. Could dolphins or whales have done it too, if they were land creatures?