Consider the following sentences:
We can probably all agree on the fact that these are all perfectly grammatical sentences. Not only are they grammatical, every person speaking English will have no problem understanding the meaning of any of these sentences. For instance, no person will think the sentence "I could have been reading the book and you could too" implies that you could have mowed the lawn or could have been painting the ceiling. Apparently it is possible (at least in English), to leave out VP constituents. This phenomenon is commonly referred to by linguists as VP ellipsis or simply ellipsis. What is left over after leaving out the VPs is called the remnant.
Now it would be very naive too syntactically represent the "you could too" part (the remnant) as something like this:
Of course "could" is a modal verb and may not be used independently as if it is a main verb like was done here. Try to find a better way to syntactically represent this. Use the Penn Treebank to find examples of ellipsis (you should be able to find at least two of them). Pay close example to the remnant and what is being done with it.
Having trouble finding any examples? As a last resort you may click the Explanation button for some examples