To generate nanostructured vehicles with tunable internal organization, the structural phase behavior of a self-assembled amphiphilic mixture involving poly(ethylene glycol) monooleate (MO-PEG) and glycerol monooleate (MO) is studied in excess aqueous medium by time-resolved small-angle X-ray scattering (SAXS) in the temperature range from 1 to 68 degrees C. The SAXS data indicate miscibility of the two components in lamellar and nonlamellar soft-matter nanostructures. The functionalization of the MO assemblies by a MO-PEG amphiphile, which has a flexible large hydrophilic moiety, appears to hinder the epitaxial growth of a double diamond (D) cubic lattice from the lamellar (L) bilayer structure during the thermal phase transition. The incorporated MO-PEG additive is found to facilitate the formation of structural intermediates. They exhibit greater characteristic spacings and large diffusive scattering in broad temperature and time intervals. Their features are compared with those of swollen long-living intermediates in MO/octylglucoside assemblies. A conclusion can be drawn that long-living intermediate states can be equilibrium stabilized in two- or multicomponent amphiphilic systems. Their role as cubic phase precursors is to smooth the structural distortions arising from curvature mismatch between flat and curved regions. The considered MO-PEG functionalized assemblies may be useful for preparation of sterically stabilized liquid-crystalline nanovehicles for confinement of therapeutic biomolecules.