Period doubling (PD) and the merging of multiple dissipative-soliton-resonance (DSR) pulses are investigated in a fiber laser. Depending on the initial conditions and operation settings, various PDs of multiple DSR pulses are achieved. For two coexisting DSR pulses, we observe PD on both pulses or PD on a single pulse while the other pulse maintains period one. For three coexisting DSR pulses, PD on all pulses or PD on one/two pulse(s) are achieved when the other pulses maintain period one. It is observed that excessively increasing the pump power could destroy the PD behavior. Within certain parameters, PD behavior can be maintained by increasing the pump power. Apart from the appearance of PD, it is found that two DSR pulses may merge into a single DSR pulse if the pulse interval is small enough during pump power increase.