Procedure for a board game with individual control over the same objects

Hi, I'm new to unity and I'm currently working on the multiplayer aspect. I made a little game based on a famous boardgame called "Raisende Robots" where you must pick objects by moving orthogonally 4 color robots across the board.
My solo version works well. I dropped the pickups and the robots on the scene then i individually disabled them to enable one of them at a time, and select a new one to enable when the player picked the active one.
I'm struggling to understand concepts of...

Procedure for a board game with individual control over the same objects