Could my PSU handle two R9 290Xs? Is it even worth it?

Solution
There's no way you want to run 2 290Xs on that PSU. A single 290X can approach or even pass 300W on its own, your PSU has a max 12V output of 600W, so you're beyond peak capacity before you've even accounted for the GPUs, let alone the rest of the system.

On top of that the PSU tier list has your PSU all the way down in Tier 4: http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html
Which means that it's not absolute trash, but should really be avoided for use in any system if at all possible.
Having said that, the list has your PSU as a bronze unit yet according to your link it's Silver, so it's possible that your unit is not the same as the one in the tier list. I don't know.

750W is kind of pushing it, 850W is what you...
I strongly dislike multi-GPU due to the stutter and other issues in many games.

Start googling and you'll discover many problems even today.

POWER:
No, the 650W is not enough. Single card usage can peak over 300W:
https://www.techpowerup.com/reviews/MSI/R9_290X_Lightning/22.html

Depends on card and overclocking but we guess at worst-case scenario.

*Another rule of thumb is whether you have enough 6/8-pin PCIe connectors for the cards. If not, it's a good indication there's not enough power.
 
There's no way you want to run 2 290Xs on that PSU. A single 290X can approach or even pass 300W on its own, your PSU has a max 12V output of 600W, so you're beyond peak capacity before you've even accounted for the GPUs, let alone the rest of the system.

On top of that the PSU tier list has your PSU all the way down in Tier 4: http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html
Which means that it's not absolute trash, but should really be avoided for use in any system if at all possible.
Having said that, the list has your PSU as a bronze unit yet according to your link it's Silver, so it's possible that your unit is not the same as the one in the tier list. I don't know.

750W is kind of pushing it, 850W is what you want really, here's a good one for $65 US if you can use the rebate: http://pcpartpicker.com/part/evga-power-supply-110b20850v1

As long as you're running 1440p or 144hz to justify a second 290X, then your CPU won't often hold you back. It's totally not worth it for 1080p @ 60 gaming though.
 
Solution
http://www.guru3d.com/articles-pages/radeon-r9-290x-crossfire-vs-sli-review-benchmarks,4.html

Different cards and the max draw was 661W. So a 750W would be the minimum but an 850W would be better.

*Again though, I dislike Crossfire. I forgot to add that not all games support Crossfire, and many due to AMD's financial situation may take a while to get support after launch or again may have issues.

My advice for upgrading is to buy a GTX980Ti and sell your old card, though at this point I'd wait and buy an NVidia Pascal version a few months after launch. Yes, perhaps up to a year away but then the R9-290X is still a good card especially if you properly tweak your games.

(I'd also think about eventually getting a FreeSync or GSync monitor. GSync is better though many think they're similar. The main advantage IMO is how it handles the low end such as sub-30FPS. That's a lot smoother than AMD's solution. People say "but you won't game below 30FPS"... well, you often do. Any time you see noticeable STUTTER you've dropped temporarily below 30FPS for sure and it's those times when you benefit the MOST from a smoother experience.)