It's entirely down to Nintendo, if they want to break the record then Switch will. However if they do a Sony PS4 and never drop the price when sales significantly decline then cut production once the successor hits the market then Switch will be 3rd place.

It depends on if it can reach 125 million by the end of the fiscal year, and have another 20+ million year next year. If so, it has a shot

Exactly, that's why I said console sale numbers don't really matter to the company. 

If Nintendo can push off a Switch successor until 2025, I can definitely see it passing PS2 & DS. Switch could even potentially beat PS4+Xbox One combined (about 169 million max for those 2 combined most likely).

Frankly, I can't see a successor launching before 2025 (and I hope it doesn't get announced until 2025 as well). I actually think we will get a Switch revision in March 2023 alongside BOTW 2. Basically a Game Boy Color/DSi/New 3DS sort of situation.

Late 2025 is also good enough to guarantee that the successor has a solid first year. We could see 2D Mario, Mario Kart and Pokemon Gen 10 in Late 2025 for the new system. Although I could see Gen 10 still being playable on the regular Switch akin to how GS was playable on GBC & GB (even though Switch to a Switch successor is a new generation whereas GB to GBC seemingly is not). Then we could see games like Animal Crossing and Smash Bros in 2026. Honestly, Switch 2 has a good chance of having a bigger first year than Switch did.

The earliest I can see a Switch successor coming is Holiday 2024, but I can also see it being pushed to 2025.
Since there's no competition for Nintendo to worry about like with the PSP or Vita, which is why the DS came out in 2004 and effectively cut the GBA's life short, or why the 3DS came out in 2011 even thought the DS was coming off a 20 million year and still had plenty of juice left.
This time around, since there's no real, direct competition in the handheld (or hybrid) market, they can take their time and squeeze every last drop they can out of the Switch before they formally move on to the next system.

As cool as it would be, I can't see Nintendo holding off on a Switch successor long enough for it to pass PS2 and DS.
The Switch could easily hold out til 2024 given its momentum, but it would be 7 years old by March that year, and Nintendo pretty much never lets their systems go that long before replacing them.

I still expect a successor before the end of 2023. They'd be smarter to wait in my opinion, but Nintendo very often don't do the smartest thing.

Still, third of all time is a hell of an achievement nonetheless.

My thoughts  exactly. 

I agree.  Also, Nintendo's profits from the past two fiscal years are around twice what they were during the Wii/DS period's best years.  They really should be in no hurry to replace the Switch.  Whenever a new system releases there is a lot of uncertainty about how profitable it can be.  Meanwhile, they currently have their most profitable system ever.  I don't think they are going to replace it until it looks like profits (and software sales) have seriously declined from the current high.  Because of that I'd agree that 2025 looks like the most likely year for a successor.

Time will tell.  You might be right, you might be wrong.  It will be interesting to see what Nintendo does.

Personally I would be very surprised if a Switch 2 doesn't happen in 2023/2024.  

No that is not true. Wii/DS best year profited 550 billion yen and that's about the same currently. Even without inflation calculated, the past two fiscal year are not twice of what the Wii/DS era was.