Formal:
* Concurrent processing
* Parallel processing
* Multithreading
* Simultaneous processing
Informal:
* Juggling
* Doing two things at once
* Handling multiple tasks
* Balancing multiple responsibilities
* Wearing many hats
More specific:
* Time-sharing (when referring to computer processes)
* Switching tasks (when referring to switching between different tasks)
* Multitasking skills (when referring to someone's ability to multitask)
The best synonym will depend on the specific context and what you're trying to convey.