Chaining compressors lets each stage handle a different dynamic task
When a source has two distinct dynamic problems — say high-ratio control of extreme peaks plus broad low-ratio smoothing — one compressor cannot serve both optimally. Chaining compressors in series, each dedicated to one task, is common commercial practice and also lets you achieve heavy overall reduction without driving any single unit hard, and blend the sonic characters of several characterful units (common on vocals).
Examples
A vocal through an LA3A pummelled with 20 dB, then an SSL with a fast attack to smooth the extra attack the LA3A adds, controls both overall level and transients without one unit fighting the other.
Assessment
Explain why chaining two compressors with different settings beats a single compressor for a signal with both peak transients and broad dynamic variation.