How to sync music onto an iPhone from a different computer?

My friend put music onto my phone from her computer and i want to put music from my computer onto my phone, however the itunes won't let me.

Just sync your iPhone with your iTunes, then the music on your computer will be synced to iPhone, however, in this way you'll lose the music which synced from your friend's computer.

By the way, we would like to use leawo iTransfer to add music on iPhone, iPod from different computers, as which can keep the previous music on iPhone or iPod.