Some pop/rock songs exhibit tonality that strongly resembles common-practice classical harmony, but which borrows from diatonic modes. In other words, it is a kind of hybrid between Everett’s System 1 (common-practice classical) and System 2 (based on diatonic modes). Since it is such a simply “system” of borrowing, two examples will suffice.
Radiohead’s “Everything in its Right Place” mixes elements of major-key tonality and Aeolian mode. While the introduction could be considered an example of System 5 (major triads built on members of the minor-pentatonic scale), the verse clearly clearly combines a major tonic triad with v, flat-VI, and flat-VII borrowed from Aeolian.
The Rolling Stones’ “Brown Sugar” is firmly in a major key, largely built on I, IV, and V, but regularly borrows from Aeolian for its flat-VI flat-VII I progression, heard clearly at the end of the instrumental introduction.