Perfectly possible. I have done a couple of gigs for a band as a dep like this. Everyone had in ear monitors with tier own mix. I used my own earphones. I found it fine, as I use custom earplugs so am used to having that slightly underwater feeling of my own voice, and to be honest it was great.
The other guitarists used pods into the PA, and the keys were straight in, so the only acoustic sound on stage was the drums, which were miked into the PA.
Once everyone's mix is set, it is really plug and play.
There was a FOH engineer though. I think it might by tricky to mix the FOH sound yourself with in ears in.
I reckon he best compromise is a small combo and PA support, if you operate the PA yourselves. I use a markbass mini cmd121p, guitar one uses a lanes cub 10watt valve amp, guitar 2 a koch50 watts amp but quietly, and guitar lead a fender hots rod, but again, quietly. Our drummer is nice, not too loud, and we have two great 750 watt monitors, so we have a wicked on stage sound, and the PA does all the work.
Sorry to ramble, waiting for my chicken to roast lol