Use 'visit on' when planning to be physically in someone's company, not just a virtual meetup. She was excited to visit on her best friend and catch up.
Pro Tip 2/3
Momentary Stay
'Visit on' often implies a short, casual stay rather than a long visit. Can we visit on Uncle Joe for an hour before we head home?
Pro Tip 3/3
Companionship Context
Commonly used to denote spending time to provide company, especially to someone who might be lonely. Let's visit on Mrs. Thompson this weekend; she enjoys the company.