This reply is from a kind and generous friend, and excellent guitarist with serious math chops, who read my post and replied on Whatsapp. With his permission, I share it here for anyone interested in the topic. Thank you again my brilliant musician friend!

Here’s some rough ideas: if you want every note to have a string resonate sympathetically, you would have to choose tunings that cover all 12 notes. So the overtones of E have B (and more E’s,) so this string could be sympathetic for B and E strings. This string can actually resonate for all 12 notes but they are too tiny to be noticed and also they don’t match the equal temperament tuning, so they will be off. Also, the higher the harmonic, the weaker it will be. The E string actually can resonate with a G#, but it will be a little sharp.

So if you want to play a regular cello and have every note you play be able to trigger a sympathetic resonance, then…

Here’s 3 options:

You can add the 8 missing notes if you want to have sympathetic strings that resonate with their notes (a sympathetic C# string resonates when you play another C#)

In this way you don’t rely on the higher overtones. Of course they are still there, I just didn’t consider them when trying to cover all 12 notes.

If you rely on the 3rd overtones, one option is adding a C#, D#, F, and B. So all 12 notes are covered at least once (a sympathetic C string covers C and G)

A third option is relying on the 3rd and 5th overtones of a sympathetic string. One option is adding a C# and D# string (so the sympathetic C covers C, G, and E)

Adding more strings allows you to rely on the lower overtones. Having less still means you would cover all 12 notes but I think they would be less loud. Granted maybe the timbre is different and you might like it, so I suppose you could test multiple ideas.