Inspired in a coenzyme-like behavior, an alternative mechanism to induce homochirality within a small vesicle is proposed. The system includes six different chemical species: an achiral substrate A, the enantiomeric forms L and D, a coenzyme E and two intermediate catalytic forms LE and DE. Whereas the coenzyme and the intermediate catalytic forms are trapped within the vesicle, the substrate and the two enantiomeric forms are able to diffuse selectively across the vesicle boundary. Instead of using autocatalysis, the production of new enantiomers includes two different steps, the production of intermediate catalytic species (LE, DE) and the catalytic production of new enantiomers from the substrate. Using a suitable parameterization, we found that the chiral evolution of the system is highly dependent on the total amount of coenzyme within the vesicle, regardless of whether the surrounding membrane is permeable or not. However, the existence of large flows from the outside can destabilize the homochiral state inside the vesicle. In general, homochiral states tend to arise when the amount of coenzyme is quite low, a value that can vary according to the parametrization. On the other hand, the system tends to decrease the enantiomeric excess when the coenzyme levels are high enough. In general, the appearance of homochirality is conditioned by stochastic fluctuations in coenzyme levels within the vesicle, an effect that is gradually amplified throughout the entire process of enantiomer synthesis.