Bohr's model undoubtedly was successful in giving the explanation for Hydrogen line spectra (Any doubt!! Revise validating the Bohr's Model) as well it was unable to explain the spectra of any other element except hydrogen (even helium).
The limitation was only up to single electron systems.
As far as Quantization rule of angular momentum is concerned, ten years later De Broglie gave an explanation for it and proved theoretically.
But when we recall, the second postulate doesn't put any restriction over transition between two energy states.
Any transition can take place after absorbing the required energy photon according to the model, even transitions from energy state greater than 1 to other higher energy states is possible.