We all know that the universe is flying away from the Big Bang at speeds approaching or exceeding the S.O.L. However, is it physically possible for an object to be pulling the universe away as well?
While it doesn't fully address your question, everything we can observe does seem to be being 'tugged' in a direction, and this phenomenon is known as the Dark Flow.
I suspect, however, that you mean something outside of the universe causing the expansion. This is conceptually possible in the sense that anything is possible, however it's not really compatible by various definitions.
If it were exerting a force on our universe, it would be connected in enough of a sense that the definition of 'universe' ought to include it.
Away from what? What does it mean to pull the universe?
One reason for believing expansion is that all objects show a universal redshift proportional to their distance from us. Therefore, everything is moving away from us, and the further it is, the faster it's moving away. This is completely consistent with spots on a balloon when one inflates the balloon: all points move away from one another.
If the universe were simply moving (how do we even interpret that?), the universal redshift probably wouldn't exist, right?