If you use GDAX, which is an exchange owned by Coinbase, you can convert your Bitcoin directly to Ether or Litecoin for free from BTC by placing a limit buy on the ETH/BTC or LTC/BTC order books.
Edit: However, it would probably be better if you convert your STEEM Dollars to Ethereum or Litecoin first, as they have significantly lower transaction fees compared to Bitcoin. From there you can convert to Bitcoin, Ether, or Litecoin as you wish using GDAX. If you were to use Coinbase, you would have to pay a fee on the buy and sell, which wouldn't be ideal.
my head hurts.
Ok...I looked at GDAX briefly..
it keeps saying 'institutions and professionals'.
I ain't neither.
Let's see if I can try to simplify it:
There's another exchange like Bittrex, called GDAX, that is owned by Coinbase. You can transfer your balance to and from your Coinbase account for no fee straight through GDAX. GDAX charges much lower fees than Coinbase, and lets you convert BTC to either Ether or Litecoin directly, without having to convert it to USD first. So, I'd recommend signing up for GDAX and trading through there. Let me know if there's anything that's unclear!
Edit: It does say it offers institutions and professionals the ability to trade, but you don't necessarily have to be one in order to use it. Your experience with Bittrex should be sufficient :).
AH!...that sounds promising...thank you.