An independence system is a collection $I$ of subsets of $\Omega$ such that if $A\in I$, then any subset of $A$ is in $I$. These sets are called independent.

Suppose I have an oracle for testing independence. In particular I have an ambient set $\Omega$ and an independence system $I$ of subsets of $\Omega$. I pass a subset $A$ of $\Omega$ to the oracle, and it tells me if $A\in I$. Is there an efficient algorithm for finding all maximal independent sets? I especially care about minimizing the number of calls to the oracle, which is expensive.

I implemented a brute force method (just looping over the powerset) which chokes for inputs sizes above about $n=6$. On the other hand, the Bron-Kerbosch algorithm solves exactly this problem in a special case, and my implementation of it runs quite happily up to around $n=30$. That would be plenty satisfactory to me.