I don't know the answer for doing it in Linux. (Doubtless you'll hear from some Linux heavyweight here soon.)

But if you can't do it in Linux and have access to Windows, Acronis True Image can back up a Linux partition to another MMC, and you can tell it to make the partition on the new MMC as large as you want. That is, it can accomplish exactly what you want. They offer a free 15-day trial if you don't want to buy it, and you only need to have it for a little time to accomplish your task. (Maybe there is an Acronis True Image for Linux, I don't know.)