ITunes can only be synced with one library?

I have an iPhone 4s and I recently got a new laptop.

On the iTunes (I have version 10 something) on my old laptop, whenever I buy a song it shows up directly on my iPhone without having to connect directly to the computer (I don't know how this works, but I have wi-fi). On my old computer I also have a few songs that I didn't actually buy. I got them from some friends. Those are on my iPhone but not in the Cloud.

On the iTunes on my new computer (it's version 11), a ton of songs that I bought about 5 years ago showed up. These, for some reason, are not on my old computer. I think they were saved in the cloud because now they're all showing up. I like these songs and want to keep them. So I connected my iPhone to the new computer and it either wanted to erase the library on my iPhone or to erase the library on my computer.

Basically, I want to keep the songs from my old laptop that I didn't actually purchase but I also want the new songs that showed up from the cloud to go on my iPhone. My movies aren't on my phone (I don't want them to be) and I unchecked some songs that I no longer listen to.

How can I have my iPhone be synced with this new computer, keep the songs that I didn't buy (that weren't recovered over the cloud), and keep the songs that were recovered from the cloud?

So, firstly. I think you need an iPhone data recovery software that directly recover your music from iPhone to the new computer(items can be save as.mp3 files on computer). And then you can sync your iPhone to the new computer. Second. You can restore all your icould songs to your iPhone. With the same way with iPhone data recovery software those songs can be saved on your new computer with.mp3.so all your songs are on your new computer. Thirdly, add two part of songs on your new computer to itunes. Your can have all your songs in iPhone by sync iPhone to iTunes.