How to add music on my iPhone without deleting all the current music on it?

How do I add music on my iPhone without deleting all the current music on it?

Added (1). I can't manually add songs because it's telling me that I need to "erase and sync" when I try to apply the manually add songs setting.

Get more storage

Either you have maxed out your storage or you are auto-syncing to an existing iTunes library that does not have much in it. If that is the case, turn auto-syncing off, both on your phone and on the device that holds your library.

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