I have only read the first two pages of posts to this thread, but wanted to throw in my two cents while I have the chance.
I do not make a different meal for my 2 year old (she's 26 months) but I do find myself getting up to get things for her, sometimes. For us, it generally works this way: she is in the midst of eating her food, and she'll suddenly look up and ask for "kiwi, please?" Or she'll ask for yogurt (she's used to plain yogurt; we buy it locally) or maybe applesauce. (These are all things she's asked for at least once, at one time or another. Not perpetual requests, and not to replace the dinner she's eating.)
She's also asked for "hini butter" (tahini) on Ak-Mak crackers, especially if I've offered it as a snack recently, and MANY times she's asked for cheese. Sometimes cheese and "brown crackers," which is what she calls Kashi multigrain TLC's. She goes through phases of asking for oranges a lot. And she sometimes will ask for walnuts. Every once in a very long while, she'll ask for a cup of "cow's milk." (She doesn't really drink it routinely, so this is sort of a special request, too.)
She usually asks for one thing, if she's asking (though sometimes it's a pair of things if she's used to them going together--hini butter on Ak-Mak, cheese with crackers, walnuts & cranberries, etc.)
It seems to me that her requests often make sense, nutritionally. Most times that she has asked for something like cheese or yogurt, I'm happy to get it for her because I suddenly realize I'm not certain that she's really had enough fat. And if I've got it, I will sometimes give her half an avocado in chunks (as part of her dinner) when there isn't any avocado on our plates. Not necessarily by her request, but different from our meal.
And I've noticed that she'll ask for orange or kiwi or blueberries when she's eating meat, especially if I have not combined the meat with tomatoes or some other source of Vitamin C in our meal. (Or sometimes she'll ask in addition to the tomatoes we already have.) It makes sense to me that she might need the vitamin C to improve her body's absorption of the iron in the meat, and I don't find it impossible to believe that she's asking for something out of some kind of intuitive awareness or instinct about what she needs.
Once she did ask for noodles (we had had leftover spaghetti for lunch, and she'd eaten it all and wanted more) and I remember she was upset when I told her I didn't have any. She got over it, but she was upset, expecting me to make some. The same has happened if we've been out of milk when she's asked. I guess I could have cooked pasta for her, but it seemed ridiculous since she was basically eating her meal, had other things to eat, and it would have been a fair bit of effort. So maybe I'm not acting like a short order cook with her, I don't know. If she asked for pasta during dinner (when we weren't having pasta), I can't imagine myself fixing it for her.
However, the only food she consistently doesn't seem to eat is bell peppers. She is accepting of mosts foods, at least most of the time. So it's not a matter of asking for an alternative to her dinner and me accomodating that.
True, I can't always predict what she'll eat and what she'll ignore (of the things that she likes, I mean. It seems to go in cycles: lately she hasn't seemed as crazy about pasta but more interested in eating all the other ingredients OUT of the pasta dish, which is a switch from when she would devour noodles first) but I've never known her to flat-out refuse to eat a meal that we're eating.
And sometimes I've found that giving her some chunks of cheese, or putting some frozen berries on her plate, or otherwise accomodating her request, makes her eat up something that she was previously stalled on in the meal.
I have sometimes wondered if accomodating her requests for extra things is somehow "bad," in that "maybe I'm making a mistake by following my instinct, here" kind of way. I don't know; it seems to be working for us. I find things that are compelling in various points of view expressed here. It does make me wonder.