The Diatonic algorithm is what you want.  Two additional harmonies, with both intervals constrained to scale & key.  Plus a full featured dual delay, with some unique feedback routing.  QuadraVox will give you four additional voices in scale & key.  Both have the same maximum delay time, with QV carving that time into rhythmic patterns [no feedback].  Either one can enhance the doubling illusion with short delays & panning FX.

Keep in mind that for some of those classic songs, you’re going to need a way to change the harmony intervals, or even the key / scale at certain ponts in the song.  An Aux switch, expression pedal, or MIDI can make those transitions easier, but switching between complementary presets would work.