Yes, of course, you need to use different exchanges. This makes it possible to operate a large number of cryptocurrencies and play with arbitrage.
I did try that before since prices of each coins have a slight difference if you will compare it from one exchange to another. Nowadays, it's pretty much the same but I really hate the transaction process as it is really, really slow. The possibility of playing a large number of coins through arbitrage trading can only be done if we have ultra fast lightning network, as one movement of a coin's market price can affect the whole trading parameter. One miss mark and you might be at a losing stage. I still remember (and missed) those days that I can earn around $100/day from arbitrage trading starting with a few bucks.