Can I ask for two meals for my flight without paying extra?

Yes you can ask. And I have successfully asked for extra food in the past (i.e. over the last five years and as recent as a month ago). One time when asking for a second sandwich I was even proactively offered a third one later on. I also typically ask for two beverages and never had that refused.

Of course they have no obligation to give you extra food but on a full service airline they are usually happy to. (Since you mention a first meal I assume you are on a full service airline. If you had to pay for your first meal, you'll have to pay for the second as well.)

A good strategy is to ask when they have just finished distributing meals and you have already finished yours or if you already know to be hungry, you could tell them when you get the meal that you would be interested in a second serving.
Be nice, don't interrupt and you have good chances.

Nothing wrong with asking - treating cabin crew as humans (be nice, be polite, don't stress them if you see they are busy, wait for your turn) will get you a long way. You'd be amazed what is possible. One nice passenger offsets many rude ones - be the nice one!

After seeing the comments here, I tried it myself.

Can you get it? - Yes you can, still today.

I asked in China Eastern and Korean Air, both in economy and large cabin, in 2016.

You can ask an attendant once you finish eating, and he/she kindly starts to check if they can serve it for you.

However, whether it is only a main dish or whole dish depends on the airline (and attendant oneself and also random chance). In China Eastern I only got a main dish, but I didn't like to bother to complaining about it (and it was enough), so didn't make any further actions.

When you ask, the tips by other answers would likely work to your favor; be polite, wait for the end of the distribution of meal, and don't disturb. However, I want to add one more tips; you shouldn't ask it shortly before the start of collections of finished meal. In this case, attendants have to care about only you once after they finish collecting all the other passangers' meal. So make sure your second meal is going to be collected with others'.

However, some airlines don't allow it for whatever reasons. I asked at Asiana Airlines a few times (different flight, route, and crew) but I got declined in all of them. In fact when I asked one attendant she immediately got to ask a more elderly attendant (maybe a chief) and the answer was NO. So in these airlines, you could never get an extra meal, unfortunately...

There are "extra" meals so you can certainly ask.

If you are say, a first class passenger, the extra meal will be given to you almost as a matter of course if requested. You have "first dibs" on this (and other) privileges.

If you are "coach" class, your request will be granted more often than not. A problem might arise if first class, or other coach passengers asked ahead of you, and they're "out." This might be particularly true of a certain meal, as opposed to "meals" generally.

The alternative to giving away an extra meal is that it is thrown away. Most attendants would rather give the meal to someone than to discard it. You will not be charged.

Note: This answer does not apply to "food for purchase" situations. Then you do have to pay for each meal that you eat.

I recall once that a special-order meal got mixed up and there weren't enough of them (vegetarian), so the cabin crew scrounged around and came up with a couple meals' worth of snacks and the safe sides of extra meals for that person, instead... and with the offer of more, if they were still hungry after.

Obviously this was something of a special circumstance, but the point is that those snacks would still have been on the plane, if the original meal hadn't been mixed up. If someone asked politely, there's a pretty good chance those extra snacks, or the other portions of the extra meals, could still have gone to someone else if they were still hungry even on that flight.

The cabin crew usually do their best to accommodate requests like that if you ask politely. They may be willing to put in a little more effort, like borrowing snacks from a higher class, if they know there is a reason for the request - something like a person being hungrier because they couldn't eat before the plane for whatever reason, or needing a larger meal to balance their blood sugar or to replace part of the meal they cannot eat. It might matter how long the plane ride is (and thus, how long until they know you can find something else), or probably a whole host of reasons based on how someone looks or asks, and how urgent or casual the crew thinks the request is.

Airlines: Emirates Route: Dubai to India (CCU) Well, I got encouraged by the answers here and asked. The answer was a "No".

In the airlines defense, I asked for a Hindu meal, which maybe was limited in number. But, guess what my co-passenger told me. If you had asked it in your flight from Dubai to some western country they would be more than willing to serve you.

But here you are going back to the third world. You are lucky the "No" was not a rude one. Ouch... :(