In short, no (or I don't know it). Each transaction and contract has to pay the fee itself. You can only change the sendMode for transaction.
You can try to organise this. Some random ideas
Use contract B as proxy for all transactions to contract A and B will add some TONCOINS for payment. Also the surplus can be returned by contract A to contract B.
If contract A has any transaction with a small amount, then A will send the transaction to contract B (also attaching the payment body) to receive some TONCOINS. B will then send back the transaction with some amount and attached body data.