My kid has a habit of using too much paper. I have tried various methods. The one that worked the most consistant. As said above this just moves the problem further down the line, but solves it at the bowl side.

Take a normal floor mop, put the head inside a plastic bag, use string or cable tie to seal the top of the bag around the pole, keep the mop head from getting wet. Use this as a more substantial plunger, put warm water in the toilet , plunge and flush, has worked for me everytime so far.

I have a drain cleaner attachment for my pressure washer, i usually follow up with that down the sink and bath drains to break up anything remaining.

Thanks