Are there any non-standard meta objects available? I recently started playing with Meta objects again after all these years of using Blender and largely ignoring them. However, I find the available types to be extremely limited.

Are there any others available as addons, similar to how there are addons that add various mesh primitives?
No, and adding new meta-ball types to the existing system can't be done using python/addons.

(unless you count composing shapes from many metaballs).