Presently, water pollution poses a serious threat to the environment; the removal of organic pollutants from resources, especially dyes, is very important. Nanofiltration (NF) is a promising membrane method to carry out this task. In the present work, advanced supported poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) membranes were developed for NF of anionic dyes using bulk (the introduction of graphene oxide (GO) into the polymer matrix) and surface (the deposition of polyelectrolyte (PEL) layers by layer-by-layer (LbL) technique) modifications. The effect of PEL combinations (polydiallyldimethylammonium chloride/polyacrylic acid (PAA), polyethyleneimine (PEI)/PAA, and polyallylamine hydrochloride/PAA) and the number of PEL bilayers deposited by LbL method on properties of PPO-based membranes were studied by scanning electron microscopy (SEM), atomic force microscopy (AFM), and contact angle measurements. Membranes were evaluated in NF of food dye solutions in ethanol (Sunset yellow (SY), Congo red (CR), and Alphazurine (AZ)). The supported PPO membrane, modified with 0.7 wt.% GO and three PEI/PAA bilayers, exhibited optimal transport characteristics: ethanol, SY, CR, and AZ solutions permeability of 0.58, 0.57, 0.50, and 0.44 kg/(m2h atm), respectively, with a high level of rejection coefficients—58% for SY, 63% for CR, and 58% for AZ. It was shown that the combined use of bulk and surface modifications significantly improved the characteristics of the PPO membrane in NF of dyes.