If you look at the code ( three.js/src/geometries/ExtrudeGeometry.js at c12c9a166a1369cdd58622fff2aff7e3a84305d7 · mrdoob/three.js · GitHub ) you will see that extrusion is quite a complex thing.
If you want to have a very special geometry, you have to create it yourself as a custom geometry. This is not that hard with a little practice. Start with a simple example and look at corresponding examples.
From the Collection of examples from discourse.threejs.org
e.g. ProfileSurface , ColorStripeChanging
and
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BufferGeometryNonIndexed
BufferGeometryIndexed
BumblebeeMara ( geometryMouth, geometryBody, halfSphereGeometry )
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MorphBoxSphere (dynamic)
RoundEdgedBoxFlat
… and more.