Your challenge is you want to take that shape and have it animate into another shape? I would use mask, via double click that shape traced out using a mask. Thereby launching the second window (Layer window) to then see the drop drowm menu assigning your mask to that mask after enabling animate path icon in T.line. This way second mask is not started rather it will now animate to your second shape. Don't forget to move your cursor down the TL before you draw your second shape.
If you are trying to animate your asset into a another asset, see transition effects to browse in bridge for a suitable transition.
If all of this is greek to you. See this tutorial http://helpx.adobe.com/after-effects/using/animating-shape-paths-masks.html
Scroll down to here: Select masks, segments, and vertices
You can morph an one illustrator shape into another in illustrator using the blend mode, then expand the blend, then release the expanded art to layers, then import as a comp in AE and you'll have your morph from one shape to another.
Here's a zillion year old tutorial on the process.
I'm not sure I can use this method with a vector art.
I did laugh with this though "If all of this is greek to you. See this tutorial http://helpx.adobe.com/after-effects/using/animating-shape-paths-masks .html"
Because I am greek
Thank you Rick Gerard, that zillion year old tutorial helped me a lot!