Generalization of the Tower of Hanoi?

Interestingly enough, it seems that we don't actually know!

From Wikipedia:

Although the three-peg version has a simple recursive solution as outlined above, the optimal solution for the Tower of Hanoi problem with four pegs (called Reve's puzzle), let alone more pegs, is still an open problem.

There is, however, a presumed optimal solution for the puzzle with Four Spindles, also to be found in the same Wikipedia article.

The article by Demontis is totally flawed, for more details see https://doi.org/10.1142/S1793830919500496. In 2014 Thierry Bousch published a solution to The Reve's puzzle (four pegs version), see https://www.math.u-psud.fr/~bousch/preprints/revespzl.pdf. The FS conjecture for Tower of Hanoi with five or more pegs remains an open problem.