From a purely mechanical engineering perspective, you would assume only Hooke’s law would come at play. Hence, only the spring length and its stiffness constant k would be important, where the latter is determined by the spring material and its wire thickness. For that reason, I cannot recall any other typical mechanical application where “multi-stage” springs are being used.
However, this is not counting with the buckling effect, so nicely described by @flashquark above. The upper part of a two-stage spring may experience some support from the stem and buckle differently than the lower part that is perhaps more free to buckle. This gives rise to interesting effects not seen in run-of-the-mill mechanical engineering applications. In this context, two-stage springs make sense, but three-stage probably not.
Personally, I have no experience with two-stage springs —I probably should now,— but I do like the 68g GAZZEW stainless steel springs as used in the Boba U4Tx switches.
As a matter of fact, I recently replaced the shorter and narrower springs of Kaihl Silent Brown switches with those longer and wider 68g GAZZEW springs. This not only increased the actuation force, but also increased the tactility and stability of the switch.
Mind you that the stem of the “boxed” Kaihl Silent switches is in fact a hollow tube, only slightly wider in diameter than the GAZZEW spring. This offers the spring a lot of support, which will result in much less buckling at the top, compared to the bottom part of the spring. As said before, the effect of this particular spring swap feels as an improvement for this switch.