Yes, you can. I have traveled internationally and domestically with 2 large carry-ons (a roller bag and a large backpack) and I usually bring a big pillow or a large stuffed animal. They don't count it as a carry-on, especially if you are holding it and not carrying it in something like a shopping bag. Keep it with you during the flight and rest on it. If anyone questions you about it, say you are bringing it for your comfort.
Personal experience - I brought a big stuffed animal cat pillow with me to Istanbul from the US.