Assuming the other piece is a drummer, you're basically talking about a Royal Blood setup. Lots of guys on youtube showing their take on it - the Royal Blood guy himself is notoriously close-lipped about his signal path. I think the thing about it is that it only really works with songs that are written to be played with that kind of a setup. You aren't going to do Sweet Home Alabama or some such tune in any bass/drum duo and have it sound like a real song, no matter what you do. Some songs are all about the interplay between different parts, and you don't have them.
Having said that, bi-amping and pitch-shifting one chain an octave up to a guitar amp is the basic key, which you're already doing. The thing is then, to have enough interest, to think how to give yourself more options from there. One thing is to be able to mute either amp at will; I do it with a pair of JHS stutter switches. That allows some variety, muting one line at times to solo the other.
I would mostly focus on the upper-octave chain for additional possible effects. After the octave-up, I actually use TWO EHX PitchForks. One is set to a 5th up and a 50/50 blend; that allows a "power chord." The other is set an ADDITIONAL octave up, with the blend at full and the switch set at momentary; that let's me "solo" very high synthy notes above the general mix. To top it off, that chain also has an EHX C9 pedal for organ sounds, and a fuzz pedal (an SUF Civil War, in my case) for "rhythm guitar."
At the end of the day, with all this, you can still only play parts that are all in unison, and that's going to limit the songs you can do. The only other way around it that I can think of, apart from recruiting other musicians, is to get comfortable with a looper (I have one but am not very good with it), or to use backing tracks.