Can I put one circuit on two 20-amp breakers? I'm drawing too much power on just one breaker and I'm not able to run a whole new circuit right now.
First -- the job of the breaker is to protect the wire from overheating and BBQing your house. A 40A circuit would require 8AWG copper wire, not the 12AWG that is currently in your walls.
Second, you are not the circuit breaker factory, which means you have no idea how such a combination would perform, and are forbidden from doing this by NEC 240.8:
240.8 Fuses or Circuit Breakers in Parallel. Fuses and circuit breakers shall be permitted to be connected in parallel where they are factory assembled in parallel and listed as a unit. Individual fuses, circuit breakers, or combinations thereof shall not otherwise be connected in parallel.
Of course not.
You are talking about defeating circuit protection because you find it inconvenient. Obviously, this is dangerous. ThreePhaseEel goes into the gory details of how it'll burn your house down, but let's look at other options.
Map all your outlets and circuits.
Buy a half dozen night-lights at the dollar store. Turn off computers that are not laptops. Go through your house, turning off one circuit at a time, and go see which devices or outlets die when you do. I just did this, marking the breaker and outlets with different colored tape, you can label the breaker number on the outlet if you prefer. The night-lights are easy ways to see if an outlet is hot -make sure they are switched on!
Once you've mapped which circuits feed which outlets, you can check for the most common situation: someone has over-stacked one circuit while the other circuits are barely used. This can be easily fixed by rearranging things.
We had one guy who had an 850 watt gaming PC and a big laser printer, and an A/C unit too. He was very committed to make them work on the same circuit. Turns out, there was a different circuit right in the same room and he hadn't realized. Moved the laser printer to that; solved.
Rethink your energy use.
I just fired up an air conditioning unit, plugged in through a Kill-A-Watt energy monitor ($20). The Kill-a-Watt actually screamed in pain (did you know they can do that? I didn't). The A/C was drawing 17 amps. It was broken (nearly out of freon) but even fixed, it was inefficient. New units of that class draw 6 amps because their efficiency is that much better. So if you are using a decrepit old air conditioner, it needs to go into the trash, as it will cost you more in electricity than a new one costs to buy. Seriously.
A dehumidifier in the same room as an A/C unit is a mistake. A/C already dehumidifies.
All the energy you spend in a room turns into heat. You must use more energy still, to pump the heat away with an A/C unit. So any energy you save, you save twice. A tester like a Kill-a-Watt will help you identify those.
Can your laser printer live in a different room that you're not struggling to air condition? They make long Ethernet cables. (Or maybe your printer offers WiFi, so it doesn't even need a cable.)
Do you really need to use that 850 watt gaming PC right now? Can you get your work done on a laptop plugged into your big monitor (which doesn't take much energy)? Stuff like that.
One guy actually figured out that his $4000 Mac Pro pays for itself in 4 years by being more efficient than his old high end PC. And he could still run Windows on it.
Convert the circuit to 240 volts
Certain rooms in your house need a specific number of 120V outlets (e.g. within 6 feet of any point on the wall, in bedrooms). This doesn't work if converting a circuit will break any of those rules. However, it's possible in some spaces.
This will double the amount of power on the circuit, as you originally hoped. However, the rules are byzantine. Each of the loads on the circuit must be 1440 watts (6 amps) or more, and it can't include lamps. I would argue that a qualifying load could be a 1500W step-down transformer with multiple loads plugged into it. But your local electrical inspector might disagree.
In this case, you change every outlet to NEMA 6-15 or 6-20, remark the wire formerly known as "neutral" to be another hot, and punch it down into a 2-pole 20A breaker.
Split it up & add an additional 20A circuit & use the other 20A circuit for what you were going to use it for. Refer to NEC for further info