Can you respond to a counterspell with another counterspell targeting the first one?

When you cast a counterspell, it goes on the stack as a spell. Before it resolves, both players receive priority and may cast more spells or activate abilities (CR 117.3). This means your opponent — or you — can respond by casting another counterspell that targets the first one.

Counterspells target spells on the stack (CR 114.1). A spell on the stack is a legal target for another spell that says 'counter target spell,' so the second counterspell can absolutely target the first (CR 608.2b).

The stack resolves last-in, first-out (CR 405.6b). So if Player A casts Counterspell targeting your creature spell, you cast Negate targeting Player A's Counterspell — Negate resolves first, countering the Counterspell, which is then removed from the stack. Your creature spell is no longer threatened and will resolve normally.

This can continue indefinitely — players may keep responding with more counterspells, bounce spells, or other instants, creating a 'counter war.' Each new spell is placed on top of the stack and resolves before the ones below it.

Note: if the second counterspell's target (the first counterspell) somehow leaves the stack before the second resolves, the second counterspell will have an illegal target and will itself be countered by the rules (CR 608.2b).