It's double tracked. At least two completely different parts. Maybe they liked two different versions of the solo and kept both. For the rest it's mostly a pretty trebly amp. Lots of reverb, no delay. Try a Plexi1, dime the treble and the presence, cut back on the sag, depth and warmth. 4x12 20W cabs. 3 second LG Plate reverb with the mix at 35%. Have at it with a strat bridge pickup.
The parts are so much different. At the beginning they harmonize a third, then they go unison, then harmonize two notes, then it delays and it ends in a harmony again.
You can't copy it, maybe trick it with a harmonizer and a delay and a foot pedal set to morph between them in the middle.
The single notes preceding the solo and the ending sound like an envelope filter/touchwah.
The verse parts have a leslie/phaser type sound. The 'rotary' in the Axe-FX gets pretty close on default settings.
Fun, this.
I like that song.