EPDA · Tree-adjoining (mildly context-sensitive)
aⁿbⁿcⁿdⁿ — four counts, one stack of stacks
Two independent stacks would be Turing power; one stack whose elements are stacks is exactly enough. The a's and b's are matched on the working stack while the c's and d's are parked beneath it, to be picked up in order once it is gone.
The author’s examples, run
abcd → acceptaabbccdd → acceptaaabbbcccddd → acceptaabbcd → rejectabccdd → rejectabcdd → rejectaabbccd → rejectabdc → reject