If you control two Panharmonicons, do triggered abilities from entering the battlefield trigger three times or four times?

Panharmonicon's ability reads: 'If an artifact or creature entering the battlefield causes a triggered ability of a permanent you control to trigger, that ability triggers an additional time.' Each Panharmonicon independently adds one additional trigger to the original trigger event.

Under CR 603.2 and the layering of replacement/additional-trigger effects, the process works like this: the entering permanent causes the ability to trigger once (the normal trigger). The first Panharmonicon sees that trigger and adds one more, making two. The second Panharmonicon independently sees that same original trigger event and adds one more, making three total. Neither Panharmonicon 'sees' the copies generated by the other — they each only react to the original triggering event, not to each other's additions.

This is distinct from how copy effects can sometimes cascade, because Panharmonicon creates additional instances of the trigger rather than copying an already-generated trigger on the stack. The two replacement/addition effects are applied simultaneously, each contributing +1 to the base of 1.

Concrete example: You control two Panharmonicons and a Solemn Simulacrum enters the battlefield under your control. Solemn Simulacrum's 'search for a basic land' trigger fires once normally. Panharmonicon #1 adds a second trigger. Panharmonicon #2 adds a third trigger. You end up searching your library for a basic land three times total — not four.

Reference rule CR 603.2 governs how triggered abilities trigger, and the Panharmonicon template is a 'triggers an additional time' effect, meaning each copy of the card contributes exactly +1 to the trigger count independently.