A professor gave us this problem, which I could not solve: Reduce VC to 2VC. (Prove that 2VC is NPC)
Definition: 2VC gets G, and K, and returns true if there are 2 different VC in size K in G. (In the same way that double clique finds 2 clicks in size K)
Note: The problem was not written in English, so my translation might be slightly mistaken.
How should I go about solving it?
So far, I tried duplicating the graph, in the same way double-clique is reduced, but it doesn't help.
Add two new vertices joined by an edge, and adjust $k$ appropriately.