Altium net designator like option?
There is no need to duplicate the sheet. Just create a top sheet (or use the sheet where the current source is used) and create multiple instances. This will - depening on what you have set in Project Properties - yield multiple instances of the very same sheet on your PCB. I recommend NOT using the REPEAT statement if it's just three of them. Just add three instances of the sheet symbol and you will get net names like R1A, R1B, R1C, C12A, C12B, C12C (how these net labels are generated exactly is configured in the project options dialog).

Be aware that you need a project type of "Hierarchical" or "Auto" for this to work (this is also in Project Options and can be set at any time).

This will also allo the use of the Copy Room Format feature in the PCB which will align the three instances in a similar way once you're completed one of them.

As @SpehroPefhany pointed out, it's officially called multi-channel design and it has its issues but in general it's quite nice.