Older work with HTM did consider multiple levels. The H of HTM is hierarchy.
Since that time the work has pulled back from “H” to focus on loading a single level with as much function as possible. That has brought the current “thousand brains” view as the state of the art.
Now if only these “thousand brains” could work together with hierarchy.
I think that the direction of future work will have to move back to hierarchy to see the full power of HTM blossom.
Right now there are questions regarding the connections between layers 2/3 and 4 and from what I can see this is being considered with a strong focus on the local computation. If you pull back and notice that the map to map connections use L2/3 as the connection point this may cause a rethink on how the column fits in a larger system.
More plainly - if the column is part of a larger system the function locally has to fit into this larger picture. Making more of an effort to bring in “H” will inform consideration of what is being computed locally.
I am encouraged that there is news that the elves at Numenta are considering the connections to the thalamus in the lower levels. If this widening of focus is extended to the L2/3-to-L2/3 connections all the better.