Is there an upper limit to how large of a dose of fentanyl before narcan stops working

I’ve heard stories from EMTs of finding someone who OD’d and the EMT having to give them multiple doses of narcan.

My understanding is the u-opioid receptor is the one that causes respiratory depression. Naloxone has a stronger binding affinity for the u-opioid receptor than fentanyl, so it should displace fentanyl from the receptor.

A single administration of naloxone at a relatively high dose of 2 mg by intravenous injection has been found to produce brain MOR blockade of 80% at 5 minutes, 47% at 2 hours, 44% at 4 hours, and 8% at 8 hours.[72] A low dose (2 μg/kg) produced brain MOR blockade of 42% at 5 minutes, 36% at 2 hours, 33% at 4 hours, and 10% at 8 hours.[72] Intranasal administration of naloxone via nasal spray has likewise been found to rapidly occupy brain MORs, with peak occupancy occurring at 20 minutes, peak occupancies of 67% at a dose of 2 mg and 85% with 4 mg, and an estimated half-life of occupancy disappearance of approximately 100 minutes (1.67 hours).[73][74]

So at 4mg, the peak receptor occupancy is at 85%. But what happens if someone takes an extremely large dose of fentanyl like 20mg or more? Is naloxone enough to block the receptors and prevent death by respiratory depression?

Naloxone is much shorter-acting than fentanyl, and other opiates, and that’s the main reason why EMTs, etc. have to give multiple doses.