Yes. Some platforms allow margin trading and often with leverage as well. An example of a platform that offers this is
BitMex, but there aren't any with a particularly good reputation that I can see people with a large amount of money trusting.
It's obviously possible, but the demand for it isn't high enough yet for the majority of platforms to try implementing significant leverage. Some of them have a small amount of leverage (2-3x leverage like GDAX and Bitfinex), but not crazy amounts like there sometimes is on Forex markets.
Considering the crazy volatility in the BTC market, leverage is a pretty bad idea. It's fine for people to have that option but it's very risky for the exchange, so they have to set automatic stop losses to make sure they recoup the money if you fail.
