Alright, how about this:
The Sovereign Military Order of Malta ends up in the territory of the Vatican. That makes it an enclave inside another enclave, both surrounded by just one other sovereign state.
Lets add another layer: Either Italian unification doesn't incorporate Naples, or Italy is broken up in WW2 (I like this option better). Either way, South Italy does not want North Italy to include Rome, for diplomatic reasons. It is decided that the eternal city will be an international city, and effectively becomes an independent city state that happens to be surrounded ny North Italy.
Combine that with my proposal in the first paragraph, and you have a state inside a state inside a state inside a state.