I am guessing you are very new to AE. I have no idea what kind of animation is applied to the box but if it is just movement then you can simply add your new layer, drag it into position, then parent the new layer to the box.
When you have questions about a layer or you want to figure out what is going on in that layer select the layer and press the U key twice to reveal all modified properties. If your screenshot had shown the modified properties of the box layer I could answer the question without any problem.
If there are more things going on and just position changes then create a new comp that is exactly the same size as the box and add a layer that is the same color as the box. Add your new layer (Twitter logo) to this new comp. I would name it something like "new box."
Now return to your main comp and select the box layer.
Find your new comp with the box and Twitter layer in the project panel. Select the new comp and hold down the Alt/Option Key and drag it from the project panel to the timeline. If your box layer was selected in the timeline then this should replace the box layer with the new comp and all of the animation and effects will stay in place.
Because you did not know how to do that I would suggest that you spend some time learning the basics. Any student I have ever head would know how to do this after the first class because changing elements in a composition is the most basic of basic skills you need to know how to do.
Place the Twitter logo above the box layer and parent it to the box.