Warm, fat cleans? There are many ways to get there.
Look at changing the IR: That's more of a rabbit hole than I want to go into here regarding specific recommendations: but that change can enhance the body of the ODS, or if you want to stay close to the classic Fender cleans - and are willing to trade off some of the Jensen bite and sparkle for thickness. Try a closed back instead of open, or a 4x12 if you're used to a smaller cabinet.
As far as amps: EL84 amps are a great sandbox to play in: The AC20, as mentioned, as well as the AC15, Matchless, Ruby Rocket, and the Trainwrecks are all great fun.
Not just EL84s either. A Plexi or Deizel, for example, have great clean tones. One of my perennial favorites is the Hiwatt: With substantial gain it still stays cleanish(?) (by my admittedly loose standard of "clean"), but the plain strings thicken up with sustain and the wound strings maintain definition - fabulous overall balance.
I prefer a narrow "clean" range - because I'll want to be able to push them into (at least) a little distortion with dynamics. Adjusting the input trim is key: you don't want to hit the front end too hard, or have to set the preamp gain too low.
Not to overlook the option of a Tube Drive (Drive Block) at unity or low gain just for the thickening factor.
Also: A compressor in front of the amp: with a fairly high ratio (4:1 - 8:1), but with just small amount (20%-35%) of it mixed in parallel to give the added body without changing the dynamic feel.
A compressor is also useful when you want clean and all you want is clean: in which case its set with a high threshold to function as a limiter: In this way you can set an amp for the warmth of a little preamp saturation and avoid it overdriving on the peaks.
