  A particle rotor model, which couples nucleons in four single-$j$ shells to a
triaxial rotor core, is developed to investigate the five pairs of nearly
degenerate doublet bands recently reported in the even-even nucleus $^{136}$Nd.
The experimental energy spectra and available $B(M1)/B(E2)$ values are
successfully reproduced. The angular momentum geometries of the valence
nucleons and the core support the chiral rotation interpretations not only for
the previously reported chiral doublet, but also for the other four candidates.
Hence, $^{136}$Nd is the first even-even candidate nucleus in which the
multiple chiral doublets exist. Five pairs of chiral doublet bands in a single
nucleus is also a new record in the study of nuclear chirality.
