Lists of lists of lists

What is a good way to represent the type LoL a, being a list of lists of ... of a? The nesting level is arbitrary, but uniform over all elements of the outer list.

The case I have in mind is to apply a grouping on the members of a list, and then to apply a next grouping on each subgroup, and so on. It is not known up front how many groupings one will have to apply. Hence:

rGroupBy :: [(a -> a -> Bool)] -> [a] -> [...[a]...]

Extra brownie points for the type signature of rGroupBy ;-)

Example:

Suppose deweyGroup i groups the elements based on the i-th number

rGroupBy [deweyGroup 1, deweyGroup 2] 
         ["1.1", "1.2.1", "1.2.2", "2.1", "2.2", "3"]

gives:

[ [ [ "1.1" ], [ "1.2.1", "1.2.2" ] ],
  [ [ "2.1" ], [ "2.2" ] ],
  [ [ "3" ] ]
]

Postscript

One day later, we have 4 excellent and complementary solutions. I'm very pleased with the answers; thank you all.