I copy from one song to another frequently. The manual process below is multi-step and works fine. I'm not aware of a way to take multiple tracks and their content of events and paste them all in one shot into a target file.
Generally speaking when I'm copying tracks they are not into exact duplicate songs, so do not have the same synths in the same order or the same tracks in the same order.
You can obviously call up a track template to get the same empty track stuff, including loaded synths etc,as an empty track (as a container to put the events into). It may also be easy to just recreate the midi or audio tracks with the same routing in the target file as as the corresponding tracks in the source song file.
In the source file, to get the event info, click on a track and ensure in the Event Inspector in your Control Bar that you can see you've selected from measure 1.
Then go to the target file and use Paste Special (Control Alt V). Paste to the track and verify you have the same measure 1 start time.
Do this procedure track by track.