If I use two identical 20-degree-rated bags, one inside the other, what would likely be the effective temperature rating? 10-degree? 0-degree? negative-10-degree?
Warning This is pure conjecture! Test this information with your gear in a safe place before using!
That being said, the basic warmth of a sleeping bag is determined by the amount of loft the fill provides. Quality of fill has a huge impact on how much loft is necessary to provide a given warmth, along with construction (i.e. baffles vs sewn through, hood quality, down distribution).
Putting all that aside, a good 20F down bag will have 4-5" of loft. So theoretically one inside the other would have 8-10". Again, theoretically that would give you ~ -10F (or perhaps even lower!).
This is assuming you don't have any down compression happening when you stuff one inside the other (i.e. you choose two bags with girths such that they don't compress each other). Since that's not likely possible, I would imagine real world performance would be quite a bit lower (maybe -5F?), and I would certainly want to test it with backups available before striking out into the wild!
In terms of clothing insulation there is the concept of the CLO. The key equation is
T = (31 − 0.155·P·R)°C
where P is 48 W/m² while sleeping, R is the number of CLOs, and T is the temperature in Celsius.
To stay warm while sleeping at 20F you need 5 CLOs (yes there is huge variation between people). If you double the bags and ignore the air gap between the bags (which will add insulation) and any compression of the insulation (which will reduce insulation), then you can just add the CLOs (just like you do with clothing). A bag with 10 CLOs will keep you "warm" while sleeping to -46.12 F.
One should obviously be careful before heading off into -46F sleeping conditions. There can be big variations depending on how warm you sleep (i.e., the P value in the equation) and if you are using a tent or snow cave. There is also the concern of the bags compressing each other and reducing the insulation properties.
While -46F seems crazy, if we compare weights, the North Face Inferno 15F weighs 1049 g with 550 g of fill while the -40F Inferno weighs 1758 g with 1249 g of identical fill. In other words a -40 degree bag has similar amounts of fill as two 15 degree bags.
I have a synthetic summer/mountain sleeping bag with the comfort of 0°C (180€) and a moderate down winter sleeping bag with the comfort of -5°C (570€). comfort meant that I can be inside in my underwear and sleep "toasty". The first (0) sleeping bag is larger so the second inserted can loft properly. I didn't do math but from experience, I was comfortable, even a bit too warm with -18°C, so I suppose I would be safe even with lower temperatures. BUT both sleeping bags weigh 2 Kg together so a better option would be to buy an expedition sleeping bag with a weight of only 1.5 Kg and a similar price for both combined. I need such a combo, maybe once or twice a year so no need for the expedition one. I case of more frequent use I would pick an expedition sleeping bag.
My experience from the winter months is:
I used 2 synthetic sleeping bags and combined them, used them at the same time. Both are 12/8/-4°C rated or perhaps one is rate a little higher 15/12/2°C. Weight is 930 g for first and 830 g for second.
8 - 4 °C. It was good, pleasant, enough warm. 0 - 4 °C. It got more unpleasant, but was bearable. -2 - 0 °C. It became even more unpleasant, I wouldn't go lower.
That was my experience with using 2 sleeping bags at the same time. That was only a few times, but in the next season I will get myself a proper winter bag. I expected more warmth using 2 bags at the same time.