Can I copy all data from one Apple ID to a new id while keeping the data in the original Apple ID?

You can try setting up Family Sharing between the IDs if you want to be able to share purchases made with the IDs.

Family Sharing.   *

ASC YouTube for Family Sharing

Family Sharing - Set up.  *

Family Sharing - Set up on iPhone.  -

Family Sharing - Set up Family Sharing in the Apple TV app.  -

To do that you would need to download any data and upload it to the second ID. Items like purchases, music, etc. cannot be transferred to a different Apple ID.