Do you have daily BMs? If not, getting on a schedule of having one per day might reduce the volume (per stool).
You could try a little more fiber in your diet, see if you get more frequent & hopefully smaller BMs. Sometimes fiber & liquid make for a stool that, although large, will be soft enough to decompose with flushing pressure.
Some of the newer toilets that save water are gutless; you could check out special high-power flushers. I thing there's even a toilet out there that sort of has a blender-type thing in the trap.
Otherwise if everything is normal, keep a supply of disposable plastic knives (do not flush) to hack up the big ones. That's less nasty/less work than having to unplug toilets & even remove/reseat them.