How can I control the audio chain within macOS? I have an audio signal coming into the Mac from an audio interface. I want to be able to control the signal flow within the Mac, routing the signal through different applications, in the order I want it to, before going out from the Mac back into the audio interface.
Loopback from Rogue Amoeba (not free unfortunately) can do this by creating several virtual interfaces that take audio from what ever input or application you want. 

You should be able to chain them together to achieve the desired effect

Loopback is not free however. 

Another option would be Soundflower. I haven't used it, and have heard it is more difficult to setup but it has the advantage of being free.