  Isochronous islands in phase space emerge in twist Hamiltonian systems as a
response to multiple resonant perturbations. According to the
Poincar\'e-Birkhoff theorem, the number of islands depends on the system
characteristics and the perturbation. We analyze, for the two-parameter
standard map, also called two-harmonic standard map, how the island chains are
modified as the perturbation amplitude increases. We identified three routes
for the transition from one chain, associated with one harmonic, to the chain
associated with the other harmonic, based on a combination of pitchfork and
saddle-node bifurcations. These routes can present intermediate island chains
configurations. Otherwise, the destruction of the islands always occurs through
the pitchfork bifurcation.
