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
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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.
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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.