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"Now it starts to get complicated. For example: if we have two THIRD CLARINETISTS in the band and one of them starts marking up their part with reminders and directions, that copy of the part is now personalised to that player. The other THIRD CLARINETIST should still be playing from an un-marked version of the file (and my indeed start putting their own mark-ups on their part). Is it possible to have multiple 'mark-up overlays' each given a personalised name of the player? "

A possible workaround for this [I have not done this, so no guaranty ]:
1-Edit [tap center of display>create snippets [circle w/triangle, bottom of display]. 

2-After creating the snippet/CSV, start at the main library, select the appropriate song [snippet] >edit song>rearrange pages [square w/mountains icon at display bottom]> Save as new song [overflow [3 dots top of display]. 

This should give you two identical copies, be sure to name one for each instrument. 

I think you could do this using copy but I could not find it. 

Unfortunately, I don't know how this will affect the original pdf so you may need to learn how to load multi-pdf's songs via CSV. I think CSV's load each song separately so annotations are separate while snippets annotations affect the basic multi-pdf, which you probably don't want. 

Assuming CSV's work, the second part of the workaround should be usable. 

The rest I think you can do as described by BRX above.