Dissipative solitons (DSs) usually play an important role in understanding the intricate phenomena in various nonlinear systems. As a special regime in the dissipative system, noise-like pulses (NLPs) can have typical characteristics of ultra-broad and smooth spectrum, high pulse energy and low temporal coherence, making them a good candidate for many applications, including supercontinuum generation, industrial micromachining and optical metrology. In this paper, a noteworthy observation concerning the dynamics on coexistence of the multiple solitons and NLPs operation in a net-normal-dispersion passively mode-locked fiber laser based on nonlinear amplifying loop mirror (NALM) is reported. In the experiment, the stable DSs can be easily obtained at a proper pump power. When appropriately increasing the pump power and changing the polarization state, the DS operation can change to the NLP regime. When the fiber laser operates in an NLP state, the single soliton bunch contains multiple pulses with different temporal spacings. And the temporal interval between the adjacent pulses is in a range of several hundred picoseconds, which decreases from left to right with time changing, indicating that there are long-distance interactions among these multiple pulses and they gradually become stronger and stronger. Besides, the pulse number of single soliton bunches on the NLP operation increases almost linearly with pump power increasing. At a maximum pump power, there are eight pulses inside the single soliton bunch. With the increase of pump power, the average output power and pulse energy of these multiple solitons in the NLP state increase. The maximum average output power and pulse energy are 12.3 mW and 1.65 nJ, respectively. In addition, the real-time dynamic evolution of these multiple solitons in the NLP state is investigated by using the time-stretch dispersive Fourier-transform method. The results show that all the pulses in NLP regime actually consist of chaotic noise waves with stochastic intensities. We believe that this paper will be of significance in studying ultrafast fiber lasers and nonlinear optics. Moreover, we hope that these findings will be helpful in understanding the physical mechanism of NLPs and paving the way for exploring other complex soliton dynamics.