Should I remove old electrical wiring if over boarding ceiling?

[Andrew So]

Hi, 

I am rehabber new to the scene. Currently, I am doing rehabbing my first property and it's a building built in the 1900's and need some advice on redoing the electrical system.

The building is currently single metered for the entire building with wires in the ceiling. I am trying to make separate meters for each unit. Would I be able to over board directly onto the ceiling and run the new lines behind it without removing the old lines?

Thank you for any and all input!