Yes you can. The diagram below shows how ... The first receptacle gets its power into the top screws but I left off the wires to simplify the diagram. The hot, neutral and ground (omitted for simplicity) exit through the bottom of the receptacle.
You have access to all those wires.
For the new receptacle, simply add your conductors as indicated. The black dots are wire nuts. The new receptacle terminates.
How does that help you?