Yeah there's a client-side check that prevents this.
not always the case and can be done, check this tx address 1FMmEBoj7
https://blockchain.info/tx/85aa6103f6314cd81c1596299ddfc5cfd768e8aff93b310dba35df400ae7ff7c?show_adv=true
https://www.blocktrail.com/BTC/tx/85aa6103f6314cd81c1596299ddfc5cfd768e8aff93b310dba35df400ae7ff7c
I took this from another thread, he encountered a problem the exchange receiver only recognize one of them
eventhough possible why you want wasting txfee/bytes and possible problem (as stated above)
You can do this by creating a raw transaction.