How to add single songs to my iPhone without deleting the rest of the ones there?

I have an 32 gig iPhone 4 with iOS 6.0.1. I have an iTunes library of about 2800 songs and I'm really having a hard time getting them to sync. I had them all on there at one point with at least 5 gigs left off space and downloaded a few more songs through my computer. When trying to sync now I can only sync about 2000-2300 and the other 500-800 just don't sync. I get an error saying all songs could not be synced. I have removed all songs from my iTunes library on my phone and re-added them all to make sure there was no "dead ends" or songs that had been deleted or moved from the folders. If I get about 2000 on their and then try to manually add the rest it just deletes everything and start over even though I have "manually manage music and videos" selected. I'm missing something.lets say I have 1800 songs and want to add 200 more without starting over and syncing all at once how do I add the 200 without deleting the other 1800? Help please! I'm sure I'm following the instructions on apples support page properly but I can only either do all or none.

When you find the one you want to delegate slide it to the left and it should say delete

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