This work investigates the elongational flow of aqueous solutions of mixtures of a high-molecular-weight poly(ethylene oxide) (PEO) and sodium dodecyl sulfate (SDS). The formation of micellar aggregates of SDS along the PEO chain results in an increase in the strength of the extension thickening of the PEO solutions. This is especially pronounced under conditions in which the PEO molecules form transient entanglements in the flow field. The minimum PEO concentration required to form intermolecular entanglements is substantially reduced in the presence of micellar aggregates. This effect becomes quantitatively less important in solutions with NaCl, which suggests PEO coil contraction due to electrostatic screening of micellar aggregates. However, once extension thickening starts in the presence of NaCl, the growth of pressure drop is more abrupt than without salt, which suggests stronger interactions between PEO coils with attached aggregates. The critical aggregation concentrations of PEO/SDS and PEO/SDS/NaCl solutions agree with those reported in the literature, which were obtained by means of different experimental techniques. However, the saturation of the surfactant effect is attained at lower surfactant concentrations than the polymer saturation point previously reported. This might reflect a low sensitivity of the extension thickening effect to the amount of surfactant bound to the polymer chain as the saturation point is approached.