# The class of grammars recognizable by backtracking recursive-descent parsers

It is easy to show that there exists a grammar that can be parsed by a recursive-descent parser with backtracking but is not an $$\text{LL}(k)$$ grammar (consider any grammar with a production featuring two alternatives starting with $$k$$ occurrences of the same terminal).

My question is the following: Is there an identifiable strict superset of $$\bigcup_{k \in \mathbb{N}} \text{LL}(k)$$ grammars that can be parsed by a backtracking recursive-descent parser, regardless of complexity?

If yes, is the maximal strict superset also identifiable?