The only way that would work if it was like a Series S|X situation. Where every game is basically the same on both platforms, but one gets scaled down. 

I'm almost sure that's what MS is going to do - the handheld will be their new Series S.

Funny question guys. If Playstation released a new handheld that could play games natively. What name do you think would fit the best? I think the best name would be
Playstation Refined.

Really cool seeing Helldivers 2 blow up.

222k players right now.

PSP2

Unless the Vita counts as two, then maybe just PSP again.

Regardless of what happens - I hope all 3 makers consider b/c and future proofing libraries.

PlayStation Portal is initialed PSP lol

PlayStation Viter

I'm not so sure XB will make a handheld. It wouldn't surprise me that much if they did, because it does sort of fit into play everywhere, but after todays podcast update, their focus was still clearly on performance and power in the future. That doesn't mean they can't have an XBSX2 next gen along with an XBS M or H (mobile/handheld), but after everything else they hinted at, they didn't seem to hint at different hardware at all. They also focused on what made the most business sense for XB, and putting XB games or GP on other (mobile and handheld) hardware makes more sense first, if they can grow that way.

Now if they do decide to make a handheld, I can't see them dropping the S model for an MH model. I'd guess they would just add it to the lineup. 3 'consoles' is pushing the limit as to consumer confusion, but if 1 is a handheld (could be a hybrid), that makes it a bit easier, having 2 consoles and 1 handheld. The XBSS is selling way too good to drop, and how many of those players will downgrade to an MH or upgrade to an X? The X has already been available, though was a bit hard to get for a while, yet even now, X sales aren't taking off. Unless XB feels really confident that most S owners and new customers will just get a MH, they won't and shouldn't drop the S model.

Now if I were XB, and we were going to do the handheld next gen, I'd split the difference between the X and S and make an (E?) model for $400, plus have an M handheld for $300-$400. Having the most powerful hardware isn't worth it, plus it would make game development a bit easier for the MH if the console isn't miles ahead in terms of performance. $400 is also the sweet spot still. The main problem here would be how many hardcore X customers would go to PC and use Steam or go to PS(5/6)? With XB being so digital now, it would make it difficult to leave the XB ecosystem one way or another. If they just got a high end PC and played GP there, it wouldn't be a loss for XB at all.

I know handheld and mobile are seen more as handheld vs phone, but they surely couldn't call it PSP now, and anything Vita related isn't smart based on it's lack of brand awareness and poor sales.

PSM (Mobile)?

If it launched around/during PS6, and can play some/all PS6 games, they could probably get away with PS6P.