It is possible.

Call Amy and Farnsworth A and F. Find two more people, X and Y. Let B(C) imply that person B has person C's mind.

So far, A and F swapped to get: A(F), F(A), X(X), Y(Y). Swaps Used: AF.

Swap A and X; F and Y. Get A(X), F(Y), X(F), Y(A). Swaps Used: AF, AX, FY.

Swap A and Y; F and X. Get A(A), F(F), X(Y), Y(X). Swaps Used: AF, AX, FY, AY, FX.

Finally, Swap X and Y to get A(A), F(F), X(X), Y(Y).

Everybody's back to normal! Well, as normal as they were to begin with.

It is possible.

Call Amy and Farnsworth A and F. Find two more people, X and Y. Let B(C) imply that person B has person C's mind. Let "Swap B and C" imply swapping whatever minds are currently in the bodies labeled B and C.

So far, A and F swapped to get: A(F), F(A), X(X), Y(Y). Swaps Used: AF.

Swap A and X; F and Y. Get A(X), F(Y), X(F), Y(A). Swaps Used: AF, AX, FY.

Swap A and Y; F and X. Get A(A), F(F), X(Y), Y(X). Swaps Used: AF, AX, FY, AY, FX.

Finally, Swap X and Y to get A(A), F(F), X(X), Y(Y).

Everybody's back to normal! Well, as normal as they were to begin with.