Your drawing is still unclear, so we still have to go by guessing - probably your compressors are not on same shaft.
You are probably talking of three process sections each associated to a single shaft, and all shafts connected by way of couplings. Which means this would be three casings.
That is a different story that three process section on same shaft, which would typically mean all are embedded in a single compressor casing. In practice, I have not seen more than two sections on a single shaft, except in multiple injection/extraction configurations. These configurations are often found in petrochemicals, refinery, LNG applications (example: propylene/ethylene or ammonia refrigerant compressors).
If each process section has a dedicated shaft / casing, then this is more of basic case for anti-surge control.
Yet, there is no such thing as a standard arrangement. Often each process section is equipped with a dedicated anti-surge valve, but not always. In some applications, you may have three process sections / casings which share a single combined anti-surge loop.
I suggest you simply need to start understanding how to set up an anti-surge control system for a single process section. That is your basic building block. If you google it, you will find lot of information about the process flow schemes, instrumentation, optional arrangements, etc.. etc.