Resolution investigation of multiplexed displacement sensors based on extrinsic fiber Fabry-Perot interferometers (EFPI) was carried out. The cases of serial and parallel configurations were considered, the analysis of the problems and the advantages of the both was performed. An analytical model, describing the resolution limits for the both configurations was developed. Serial and parallel multiplexing schemes have been experimentally implemented with 3 and 4 sensing elements, respectively. For the both configurations the achieved optical path difference (OPD) standard deviations were between 30 and 80 pm, which is, to the best of our knowledge, more than an order better than any other multiplexed EFPI resolution ever reported. A good correspondence between experimental results and analytical predictions was demonstrated. A mathematical apparatus, relating the attained sensors resolutions with the number of multiplexed sensors and the optical setup parameters was developed, also demonstrating good correspondence with the experimental results. The main origins of possible sensors cross-talk are described, with the supporting experiments, proving an importance of its consideration. Some recommendations, based on the theoretical analysis and experimental studies, dedicated to optimization of sensors resolution and elimination of the cross-talk influence are provided.