When a business or service has too many commitments, the term "overbooked" is often used. However, there are several other synonyms that could also be utilized. For example, "overloaded" can indicate a situation where there are too many tasks or projects to handle, while "swamped" can imply that someone is overwhelmed with work. "Overburdened" suggests a sense of heaviness or weight from a large workload, whereas "overscheduled" can indicate a situation where there are too many appointments or events scheduled within a particular timeframe. These synonyms can provide more descriptive language when conveying the challenges of having too many commitments.