MTGNexus

Can a spell, say Counterspell, while on the stack, have its target redirected to itself by a spell such as Imp's Mischief?

No. A spell is never a legal target for itself. However, with spell redirection spells, the "trick" is that the Mischief will cause the Counterspell to change its target to the Mischief itself. This is because Mischief is still on the stack when you are performing its instructions.

The Mischief will leave the stack so the Counterspell will not resolve since its target is gone before it tries to resolve resulting is (basically) what you are trying to accomplish anyway.

Thanks!