Is there a term for the kind of elaborating progression seen in children's songs such as "The Old Lady Who Swallowed..." and "There's a Hole in the Bottom of the Sea"? I can almost dredge one up, but I can't quite express it.
I'm trying to relate this metaphorically to a situation where one is in a hole and keeps digging -- a cascade of complications that accumulate when trying to solve what starts as a simple problem.
I could always make a direct reference to a song, like "It seemed simple enough at first, but before long we were swallowing a frog to catch a fly", but I was hoping to find a word or phrase that conveys the idea without invoking a nursery rhyme.
ETA - a suggested dupe gets only a bit toward the issue: I'm looking for something that reflects the compounding. Not just one bad thing into another, but a bad thing that you try to fix, only to introduce another, probably worse thing, and again, and so on. Out of the frying pan into the fire, out of the fire into the furnace, out of the furnace into...
FETA - I got a suggestion from someone not in this clubhouse that fits well and might spark more discussion. "The situation snowballed", invoking the accumulation of a runaway downhill tumble. Not an avalanche, just a growing problem.