Currently the footprint for the Tiered Human Silos is a regular octagon. However, the default orientation of these is such that the vertices are aligned N/E/S/W, not the faces. Now, because the vertex-to-vertex diameter of a regular octagon is larger than the face-to-face diameter, you can 'pack' silos just that little bit closer together.
How? You need to rotate each silo so that the faces, not the vertices, of the footprint are aligned N/E/S/W (assuming your plot is aligned similarly). The magic angle for this is 22.5 degrees. Of course, Horizons doesn't deal with half degree rotations, so either 22 degree, or 23 degrees, will be close enough.
The result of such 'packing' looks like...