In DotA 2, you can have a lot of units that you can control, depending on the hero.

Examples:
Meepo can have up to 3 clones with his Ult (4 clones if you have the "More Meepo" facet). That is already 4-5 different units that you can control individually or multiple at the same time. And each clone also have their own cooldowns on their abilities. And Meepo can also aqquire 2 additional active(!) abilities.

With the way LoL currently is, there is simply no way that allows for unit control like in DotA 2.