We have family in South Amercia, therefore we are almost every two years in the Andes.There you are quite often over 4000m, on a quite average hike or on several main roads in the mountains.
So the official 4000m limit of the Mini 3 is definitely not enough.
My Mavic 2 Pro was already flying without any problems around 5600m and there are videos with an Mavic 2 in the Himalaya at more than 8000m. So I'm quite sure, that the Mini 3 can cope with much more than 4000m starting height/4500 maximum in good weather. But if it won't even start from 4001m on that won't help much.

I found some "hints" that already the Mini 2 started at more than 4000m. But quite small "hints" and so far I found no hint at all about that for the Mini 3.
I asked DJI Germany, but got just an official statement "4000m height limit" without any details what happens at 4001m.
It's totally ok for me if DJI rejects any warranty oder care refresh starting over 4000m/flying pver 4500m. You can have terrible conditions and gusts also at 3000m or calm weather at 6000m.
I just want to know if our small guy starts over 4000m/if anyone here already started(!) over 4000m. And if so, up to what height/is there a real staring limit at all anywhere or can you start at any height/also in 8848m (even if this dwarf won't fly there....).
And if someone already has flown it over 4500m (flying) height, how high and with what experiences?
I would need at least starting possible up to slightly over 5000m and flying up to 5500.
Fantastic would be starting up to 6300m and flying up to 6800m, but I guess that needs a Mavic 2 and the Mini 3 won't fly anymore there...

I just want to know if our small guy starts over 4000m/if anyone here already started(!) over 4000m. And if so, up to what height/is there a real staring limit at all anywhere or can you start at any height.

The 4000m is not a hard limit, it's a service ceiling.
The drone will fly at higher altitudes, but the performance will be degraded.
Fly higher and the air is thinner and the drone has to work harder to provide sufficient lift.
The higher you go, the more that performance is degraded..

No-one can give a height at which the drone stops flying, because there's no single number to answer that question.
4000m is a height, up to which DJI are telling you that the performance will be adequate.
Beyond that height, you are on your own.

This would be totally ok for me. But until now I didn't had any garantee, that it will be at least willing to start over 4000m. DJI has not been willing to give me that statement yet.

Here in Germany I don't have the chance to test that height. And if I take it to the next visit in the Andes to find out that it won't start , it's too late (for example to return it). But as the Andes are my main use case, it won't make sense to buy it if ths isn't really sure for me.

jodijodi Posted at 9-19 04:39
This would be totally ok for me. But until now I didn't had any garantee, that it will be at least willing to start over 4000m. DJI has not been willing to give me that statement yet.

Here in Germany I don't have the chance to test that height. And if I take it to the next visit in the Andes to find out that it won't start , it's too late (for example to return it). But as the Andes are my main use case, it won't make sense to buy it if ths isn't really sure for me.

But as the Andes are my main use case, it won't make sense to buy it if this isn't really sure for me.
It will work ... but how well it will work depends on how high you fly and how low the atmospheric pressure is.

Labroides Posted at 9-19 04:26
I just want to know if our small guy starts over 4000m/if anyone here already started(!) over 4000m. And if so, up to what height/is there a real staring limit at all anywhere or can you start at any height.

The 4000m is not a hard limit, it's a service ceiling.

Worth adding, which hasn't been said. The drone will also have a reduced wind resistance at higher altitudes, not to mention it's usually a bit windier the higher up you go.

The drone is working so much harder to remain airborne at its service ceiling that the motors won't be able to fight wind speeds which it's usually capable of handling at ground level.

As I've been quite a few times with Phatnom 3 and Mavic 2 in the Andes, I know these things.  But as I said, I've had calm weather/no brainer flights in 5000-5600m (which may have been possible as well with the Mini 3). And I had gusts in narrow valleys or at mountain edges in only 2000-2500m even in sunny wheather which have "caught" any drone of these three...

Hi there. Thank you for reaching out. The Maximum ceiling level of the DJI Mini 3 Pro is 4000m for the Intelligent Flight battery and 3000m for the Intelligent Flight battery plus. If you are planning to take off above those recommended ceiling levels, we cannot guarantee that the aircraft will maintain its stability due to many reasons like the wind; the connection between the AC and RC, etc, and it is already beyond the recommended altitude. We strongly recommend flying within the recommended range and altitudes to avoid issues. Thank you for your understanding and support.