I have run BAU operations for Windows, VMware, Exchange and data centre services with teams onshore in the UK and the USA, offshore in India, and alongside several other service providers working for the same client. The model works well when the basics are written down. It fails quietly when they are not.
One queue and one owner
Every request and incident goes into one ticket queue, whoever raised it and whichever team will fix it. Each ticket has one owner at a time. When work moves between onshore and offshore, or between service providers, ownership moves in the ticket, not in an email.
Hand over at the end of every shift
A short written handover at each shift change: what is open, what is waiting on whom, what changed and what to watch. A follow-the-sun model only works if the next shift can carry on without a phone call.
Runbooks the other side can follow
If a task can only be done by one person in one time zone, it is a risk. Write runbooks as numbered steps, with what you should see after each step and what to do if you do not. Test them by asking someone in the other location to follow them.
Clear lines between service providers
When several providers support the same estate, write down who owns what: network, storage, backup, Windows, VMware, applications. A simple responsibility matrix and an escalation path stop incidents bouncing between teams while the service is down.
Measure the service, not the effort
Report against the SLAs and KPIs the client cares about: response and resolution times, change success and repeat incidents. Review them with the client and the other providers every month, and agree actions with owners and dates.
The short version
One queue, one owner per ticket, written handovers, tested runbooks, a clear map of who owns what, and regular reviews against the SLA. The location of the team matters far less than these.