How can the theory of multiple intelligences be incorporated into AI?

If anything, multiple intelligences are much more obvious in AI than in other fields, because we haven't yet unlocked how to do transfer between domains.

As an example, AlphaGo is very, very good at playing Go, but it's got basically nothing in the way of bodily-kinesthetic intelligence. But other teams have built software to control robots that does have bodily-kinesthetic intelligence, while not being good at the tasks that AlphaGo excels at.

This sort of modular intelligence is typically referred to as 'narrow AI,' whereas we use the term 'general AI' (or AGI, for Artificial General Intelligence) to refer to intelligence that we've built that can do roughly as many different kinds of things as people can do.

On possibility is a blackboard architecture. Envision each different "kind" of intelligence as a discrete agent, and let the agents collaborate using the blackboard model. Now you have an AI with multiple intelligences.

This is something I've actually been experimenting with, and while I don't have any particularly impressive results to share or anything, I hold a strong belief that an approach that is at least somewhat like this will be crucial to developing an AGI. And that is rooted in my belief that the human mind does have "multiple intelligences" and that they collaborate something like this.