Question: Will the Switch outsell the PS4, and if so when?

Answer: The PS2 was a DVD player!

Look, I get why it's been brought up, but I feel like we're off track now. The PS4 will not sell like the PS2, and the specifics of why aren't that important. It would need an insane surge of sales to occur after the release of its successor to manage that. Even if PS4 sells until 2027 and the PS5 has a Red Ring of Death level catastrophe, PS4 isn't getting within 20 million, probably not even 30 million of PS2. The Switch isn't either, even if it peaks next year instead of this year. If it does peak in 2021 instead of 2020, I could see it passing PS4, otherwise it probably won't, but it stands a great chance of outselling Wii either way, and it very much deserves it.

Whether the PS4's multimedia capabilities will help it over Switch's lack of them is kind of irrelevant at this point. We have hard sales data and patterns, we don't need to speculate about how features or lack thereof will impact sales. We've already seen how each console's features have helped it. The question at this point is what else does each system have left in its natural sales life to boost and sustain sales, what do the sales trends point to, and what events could yet change those trends. The only thing left in the PS4's life at this point is the still steady release of software, which will help, and the release of its successor, which will hurt a lot. The Switch has a lot of life ahead of it, but the sales trends aren't a slam dunk for it yet. Beyond Nintendo's continued support, I think Switch needs a little something to keep its momentum growing if it wants to beat PS4. PS4 is pretty much a known quantity at this point, but Switch still has potential to surprise us. Not "beat the DS" surprise, but certain it could manage a "beat the Gameboy and PS4" surprise.

Later than 2024 or never, it depends on how long both Ninty and 3rd parties will support it strongly. As a portable its specs are the top, and after PSV failure, Ninty will be able to decide how long NS will be the reference platform for the whole portable console market long enough to complete its planned lifecycle, but as a home console its RAM size is the bare minimum now, at least for most multiplats, one or two years after PS5 and XBTwo launch, most multiplats will arrive to require so much RAM that even the excellent streamlining Ninty consoles allow won't be enough to squeeze them into NS RAM. This will make NS lose a minority, but still a significant one, of its market, making it more long and difficult to fill the gap after, say, 2022. Still possible, but less easily than with 2020, 2021 and 2022 sales numbers. Anyhow, if NS will peak not this year, but next, the sales curve will extend longer and NS will have more chances even with its home console market part squeezing.

The only way I can see this not being Switch's peak year is if their lineup for the rest of the year is as weak as it currently appears and they have no more big system selling games after Animal Crossing, and/or if shortages become a year-long issue.

I could see another way, but I doubt it will happen: Switch not peaking this year, but next year.

For that, Switch would need several things: A strong and permanent pricecut, a new, much improved hardware revision (aka Pro model), and a killer lineup of blockbuster games from franchises not yet on the Switch (for instance Bayonetta 3, Metroid Prime 4, Paper Mario, F-Zero, a new IP...). But for all this to come together like this is doubtful. Still, I do expect 2021 to be not far below 2020 and around 2019 in terms of sales.

Shortages I think are going to be the issue. Folks are underestimating how much the coronavirus is going to mess up the games industry. Production in China is crashing based on metrics. Here's one on Steal purchases:

This will definitely impact the Switch and it may see it's weakest year on record since Nintendo still manufactures in China. Some of it has been moved to Tiawan, but not enough to make up the difference. This could help long term as supply shortages may increase demand (as consumers believe they may not be able to get on in the future and have to get it while they can). I think the peak yeah may actually be next year, depending on how everything plays out.

The good news is that this may limit PS4 sales too. The console is manufactured in Chine (story about it:https://kotaku.com/report-college-students-forced-to-make-playstation-4-1443353519_) and I haven't seen anything about them moving it like Nintendo has. Sony may not have new PS4's manufactured if manufacturing across the entire electronics industry is depressed (remember that Sony, Nintendo and Microsoft are going to be competing with phones and other devices too). 

If both the XBSX and PS5 launch at $500, the PS4 will keep selling reasonably well until the first price cuts for the new gen systems come. So, without knowing even the pricing for those systems, I don't see how we can even reliably predict where the PS4 will end up, much less whether the Switch will pass it.

That's not how things work. Ps4 is already a declining console no matter what is releasing this year.

Who said otherwise?  I said that PS4 will keep selling reasonably well, not that it will continue to sell like it did in 2017.  

But the ps4 will keep declining. Your definition of "reasonably well" must be very generous for the statement to be true.

My definition of reasonably well would be something like - better than the PS3 did after the launch of PS4.