Can you respond to your own triggered ability before it resolves?

When a triggered ability triggers, it is placed on the stack the next time a player would receive priority (CR 603.3). Once it is on the stack, the Active Player receives priority first. This means you — as the controller of the trigger — will typically be the first player who can cast spells or activate abilities in response to your own triggered ability before it resolves.

Priority passes back and forth between players (CR 117.3a). The triggered ability only resolves once all players pass priority in succession without taking any action (CR 608.1). Until that happens, any player may add more spells or abilities on top of it, forming a stack that resolves last-in, first-out.

This is very commonly relevant in competitive play. For example, imagine you control Vindicate-style effects and a Fathom Mage with an evolve trigger on the stack. You could activate a mana ability or crack a fetchland in response to your own evolve trigger — the trigger is simply sitting on the stack waiting, and you have full access to priority before it resolves.

A concrete example: Your Wrath of God resolves and triggers your opponent's Sun Titan... but suppose you have a triggered ability like Purphoros, God of the Forge's triggered ability on the stack after you played a creature. Before that trigger resolves and deals damage, you can cast an instant, activate an ability, or even add another creature to trigger Purphoros again — all sitting above the first trigger on the stack.

The key rules are CR 603.3 (triggers go on the stack), CR 117.1 (players may act when they have priority), and CR 608.1 (a spell or ability resolves only when all players pass priority). There is no rule preventing you from responding to your own triggers.