Don't let a lack of existing service capacity force you to choose between either giving up expansion plans or taking the whole facility down so you can rip out the existing service and replace it with a larger one. The former won't please upper management, and the latter could turn into the kind of project you wish you'd never undertaken (it won't please upper management, either).
Fortunately, there's a third option.
The NEC provides four circumstances in which you can add a service:
Special conditions. Offload that fire protection pump onto its own service (five other types of systems also qualify).
Special occupancies. For example, a building is so large it requires more than one service.
Capacity requirements. You'll need the electric utility and AHJ to agree.
Different characteristics. There may be a reason, such as different voltages, to use different services.