A global admin is per tenant, so you would need to manage multiple global admin users per tenant for full global admin privileges to each tenant.
However, there are ways that you can manage multiple tenants with varying levels of permissions through delegated admin privileges and M365 Lighthouse and Azure Lighthouse. These use a single identity to provide administrative access to other tenants so it would be very important to secure these accounts.
Here's some links for further reading:
https://azure.microsoft.com/en-us/services/azure-lighthouse/#overview