We investigate particular models which can be 𝒩-fold supersymmetric at specific values of a parameter in the Hamiltonians. The models to be investigated are a periodic potential and a parity-symmetric sextic triple-well potential. Through the quantitative analyses on the nonperturbative contributions to the spectra by the use of the valley method, we show how the characteristic features of 𝒩-fold supersymmetry which have been previously reported by the authors can be observed. We also clarify the difference between quasi-exactly solvable and quasi-perturbatively solvable cases in view of the dynamical property, that is, dynamical 𝒩-fold supersymmetry breaking.