BNF and Simultaneous Parsing
If the grammar is amenable to limited-lookahead bottom-up parsing, then the parallelism is more or less implicit in the parsing algorithm, and there is little to be gained from parallel computing, at least in the sense proposed in the post. A standard LALR(k) parser is deterministic; it only does a single table-lookup for each action, based on the current state, the lookahead token(s) and -- in the case of reductions -- a single state value popped from a known location on the parse stack.

That's not to say that there is no possible benefit from the availability of multiple CPUs, but I suspect that benefit would come from segmenting the input using some kind of simple lexical analysis (text inside balanced braces, for example) and constructing individual parse trees for each segment.

If the grammar itself is highly ambiguous, as is the case for natural-language parsing, then different algorithms will be employed. CYK parsing, for example, used as the basis for many probabilistic parsers, can benefit significantly from parallel processing, and it is easy to find recent (and not-so-recent) papers on the subject on the internet. I found a dozen in a few seconds, and I won't bother pasting all of them particularly since I didn't read them, but I think that this paper by Mark Johnson has some pretty impressive results.

The answer dodges around the actual question, because I think the algorithmic analysis required to efficiently parallelise chart-parsing is more sophisticated than simply exploring alternative productions in parallel. But I hope it has some utility.