General alternatives:
* Many-celled
* Complex
* Organized
* Plurisomatic (less common, more technical)
More specific alternatives, depending on context:
* Metazoan (specifically for animals)
* Eukaryotic (for organisms with complex cells, including multicellular organisms)
* Multicorporeal (meaning "having multiple bodies," but can be used metaphorically)
Ultimately, the best alternative depends on the specific context and what you want to emphasize.