Hi,
Do multiple output transactions require only one transaction fee, or do the sender pay tx fees for each output?
You only pay one fee per transaction, but the amount of the fee should be based on the size of the transaction.
Each additional output in a transaction adds approximately an additional 35 bytes to the transaction. The most common fee today is 0.0001 BTC per kilobyte. As such, you would likely want to increase the amount of the fee by 0.0001 for every 28 outputs.