Since you're talking about sets, I'm going to assume you're using one of the Invigorator apps.
Click the red ball to go to the set-up window.
Below the window choose the 3D block icon to get into the object mode.
Now, select the object in the window or in the object pop-up window.
Notice the smaller pop-up with the number in it? Choose the set number you want and hit okay.
You've now reassigned the object to another set.
Now you can select the different sets in the scene preview area and animate.