I've had a few ideas to mull over the concept of this device and have thought of a couple of ways to tackle this, all with their pros and cons.

I've roughly rounded them into 3 general Idea outlines:

Idea One

First thought is to use an Arduino Mega as a 'master' device, handling an LCD display and reading all onboard knobs and controls.

Comms between the individual effect devices would be either Serial (using the Mega's 4 Serials plus software serials if required) or i2c, depending on what is faster.

On startup the Master could try to establish connection with each of the configured ports (or scan the i2c bus for devices) to determine what devices are there and what to map controls to.

The Master then reads all control input and sends commands to the appropriate device.

I could write a library for the slave devices to ensure they can all interpret the data sent from the master and make use of it; the packet could contain data such as [ON/OFF, Control1, Control2,Control3] , which the slave device could then use to manipulate the audio data.

Idea 2

A Pi master device, with an Arduino Mega handling all input.

The Pi could then run VSTs to manipulate the audio signal, with Arduino connected via USB/Serial to then control the VST settings.

Idea 3

No traditional master device to tie together individual parts.

Perfboard soldered up with sockets to plug Arduinos in, with a 'true bypass switch' (3PDT 9 pin switch)  to control whether arduino included in signal path, with all knobs and input controls hardwired to the arduino socket. An extra arduino could be included as a slave to control an LCD.