Given P(A|B) and P(A|C), how to get or strategically approach P(A|(B & C))? Given P(A|B) and P(A|C), how to get or strategically approach P(A|(B &amp; C))?

Is there a way to approach this if it is not known whether B and C are dependent?
If not, how to get P(A|(B &amp; C)) assuming B and C are independent, or, dependent?
Suppose two $0/1$ coins $X_1,X_2$ are thrown. Let $B$ be the event $X_1 = 0$, $C$ be the event $X_2 = 0$, $A^1$ be the event $X_1 + X_2 = 0$, and $A^0$ be the event $X_1 + X_2 = 1$. Then $$P(A^0|B) = P(A^1|B) = P(A^0|C) = P(A^1|C) = 1/2$$ whereas $P(A^0|B \land C) = 0$ and $P(A^1|B\land C) = 1$.
If A and B are independent from C, then P(C|A) = P(C|B). If they are dependent, then just follow Bayes' theorem for a three event senerio.