Can you choose the order in which multiple triggered abilities from different permanents go on the stack?

When multiple triggered abilities trigger at the same time, they don't all go on the stack simultaneously. Instead, they are placed on the stack one at a time, and the order in which they are placed matters because the stack resolves last-in, first-out (LIFO). CR 603.3b and 603.3c govern this process.

Specifically, CR 603.3b states that if multiple triggered abilities are controlled by the same player and would go on the stack at the same time, that player chooses the order in which they are placed. Because the stack resolves in reverse order, whichever ability is placed on the stack last will resolve first.

If triggered abilities controlled by different players would go on the stack at the same time, CR 603.3b and the Active Player/Non-Active Player (APNAP) rule (CR 101.4) apply: the active player puts all of their triggered abilities on the stack in the order they choose, then each other player does the same in turn order. Again, the last ability placed resolves first.

Example: It is your turn (you are the active player). Both you and your opponent control a creature with a "whenever a creature enters the battlefield" trigger, and a creature enters. You first place your trigger on the stack, choosing its order freely, then your opponent places theirs on top. Your opponent's trigger resolves first because it was placed on the stack last.

Note that you can only control the order of triggers you personally control — you cannot dictate the order your opponent places their own simultaneous triggers onto the stack.