Magnetotransport studies in assemblies of chemically synthesized FeCo nanoparticles have been performed between 1.8 and 300 K. The samples display tunnel magnetoresistance (TMR), the amplitude of which ranges between 3 and 11% at low temperature, and could persist up to 0.5% at room temperature. A quantitative analysis of the resistance-temperature and current-voltage characteristics evidences the presence of cotunneling effect inside the samples, which becomes the dominant transport mechanism below 40 K. The presence of cotunneling at low temperature is clearly correlated with an increase of TMR amplitude. Interestingly, in some samples, the TMR amplitude increases with voltage, a phenomenon which is shown to be correlated with an increase of the number of junctions involved in the tunneling process. Extent of cotunneling and TMR amplitude was found to be higher in case of samples prepared by drop casting compared to those prepared by dielectrophoresis. In the former case, the assemblies are more ramified than in the latter case, indicating the importance of controlling the structural properties, and especially the mean number of neighbors of an assembly, in order to observe the cotunneling enhancement of the TMR amplitude. Apart from TMR, two other types of magnetoresistance occurring at larger magnetic field were measured. One of them could reach up to 16% in certain cases. The cotunneling enhancement of TMR amplitude in chemically synthesized nanoparticles could be used to improve response of cheap magnetic sensors elaborated using on-chip deposition of colloidal solution of magnetic nanoparticles.