What to do about chronically plugged toilet?

Your description makes me wonder... are you on a septic system perhaps??

If so, your tank is likely full, and by plunging it you could be filling your leach pipes with solids. Does the tub or sink gurgle when you plunge the toilet? Check your solids tank first. It may need to be cleaned/emptied.

If not, you have a partial obstruction somewhere in the waste line. See where the clean-outs are in your basement, start with the closest to the toilet in question, and work towards the wall it exits the home through opening each cap & snaking the line (bring a 5gal pail, as you open them, waste water may be in the line) until you've got it working normally again. If these both fail, call someone in...

You should use a snake (that is a tool), your drain is clogged. Call a plumber.

caustic soda available cheaply at DIY stores will disolve most blockages if they are organic, a platic toy may require drain rods to shift it

hand held snake. if that gets nothing, time to call a plumber

Sometimes its the toilet paper you're using. I found that my toilets did not like Angel Soft. You might find it won't clog if you flush between dropping the logs and using the paper--not so much in the bowl to go down.

Could be a foreign object, remove the toilet from the floor and check at the floor flange.

Pay particular attention to the style of "wax ring" seal where the toilet mounts to the floor, it should be replaced if the toilet is removed. Some people like to use wax rings with a centering funnel that reduces the size of the connection http://amzn.to/2yLUPxC , stuff can get stuck there easily. I prefer bare rings http://amzn.to/2z8EtLm , they seem to allow better flow.