Adding multiple items in unordered data to match a target amount

I have 3 columns of data - invoiced amounts (A), banked amounts (B) and
commission charged (C). A = B + C

For each B, there is one C.
However, there can be multiple items in A for one item of B + C.
Further, the rules for how commission is charged varies by amounts sold; I
cannot calculate C by reference to A or B (individually) with any level of
accuracy.

I'm therefore looking for a way of selecting 1 or multiple items in column
B, adding them to 1 or multiple items in column C and tracing this to 1 or
multiple items in column A.

Help would be gratefully received.