What power supply model do you have? Yes.. a 550 watt PSU might just be enough to run it (~100 watts for the CPU, ~50 watts for the motherboard, ~180 watts for each GTX 970, ~10 watts for each hard drive, ~2.5 watts for each fan and SSD), but it's not recommended at all.
If you want to run two GTX 970s, you'll want a stronger power supply of around 750 watts. It's not because it'll actually consume that much wattage, but because you don't want to be running your power supply right at the limit of what it is rated for and stressing it. A cheap 550 watt power supply might not actually put out 550 watts on the 12V rail. Yes, there are such things as cheap gold-rated power supplies, like this
Corsair 550 watt gold model which only outputs 516 watts of 12V power or this
Antec 550 watt gold model which only does 504 watts at 12V. The 12V rail is the important one that powers most of your PC. Besides, most 550 watt power supplies I've seen only have
two 6+2 PCI-E power cables maximum and
nearly every GTX 970 requires two of those, meaning you'd need to use cable adaptors to get a second set of 6+2 power cables. That's not really a good practice we recommend either.
Besides, power supplies run best when they're not at their upper limit, when considering efficiency and heat.
Any power supply efficiency chart will tell you it runs best near 50% load more than anything else. The harder a power supply works, the more heat and stress placed on the unit, and the more wear over time. Over time, a power supply will output less and less due to stress and weardown on components.
With two GTX 970s on a 550W PSU, you definitely wouldn't want to try overclocking either. Parts will draw more wattage when overclocked. The PSU might shut down or the PC won't be running well if the PSU can't supply enough wattage. Worst case scenario, the PSU shorts out or blows up and damages or kills other parts connected to it.
As for graphics card recommendations, it's hard to recommend only 2GB VRAM even for 1080p if you're looking for higher end performance. Maybe for now you might not be playing games that will use that much VRAM, or it might not even currently prove a bottleneck to performance in some situations (at medium/high settings like you said), but there's always the future to think about. Driver and game code optimizations won't completely prevent a lack of VRAM from being a problem in the future. If you really are aiming for "new-ish releases on relatively high settings", just go with 4GB and save yourself from being potentially bottlenecked or having to upgrade the graphics card prematurely in the future.
What's your budget for a new graphics card?