If you have two triggered abilities that trigger at the same time, can your opponent respond between them?

When two or more triggered abilities controlled by the same player trigger at the same time, they are all placed on the stack together during the next time a player would receive priority. The controller of those triggers chooses the order in which they are placed on the stack (CR 603.3b). This entire process happens before anyone receives priority to respond.

Once both triggers are on the stack (in the order you chose), play proceeds normally — your opponent can respond to the top trigger on the stack, but by that point both triggers are already waiting to resolve. There is no window between the two triggers being 'put on the stack' where anyone can act.

It is worth noting that after each trigger resolves, players do receive priority again. So your opponent can respond after the first trigger resolves and before the second one resolves. The restriction is only on the placement step — they cannot slip in between the two triggers being added to the stack.

Concrete example: You control Purphoros, God of the Forge and Warstorm Surge. You play a creature, causing both triggers to trigger simultaneously. You stack them however you like (say, Warstorm Surge on top). Your opponent cannot respond before Purphoros's trigger is also placed on the stack — both are on the stack before anyone gets priority. Your opponent may then respond to Warstorm Surge's trigger, or let it resolve, then respond before Purphoros's trigger resolves.

Relevant rules: CR 603.3 covers when triggered abilities trigger and are placed on the stack; CR 603.3b specifies that the active player orders simultaneous triggers they control; CR 116.3b establishes that players only receive priority after the stack is fully updated.