An eGPU is an additional graphic card, that is connected to the computer via a Thunderbolt/USB-C cable.
You can find many information on this post by Apple, and on the eGPU.io website.
For example, the combo Razor Core X + AMD Vega 56 works great for less than 700€.
It's plug-and-play (less than 5 minutes, no screwdriver needed), and it features 4 to 6 HDMI/DisplayPort outputs depending on model.
To use an eGPU, we recommand to use macOS 10.13.6 or higher, and the HAP codec.
It is also important to connect all your displays to the same GPU, and run Millumin from this very same GPU.
In the case of an eGPU, you should not use your internal display to show Millumin's interface, but rather run Millumin from a display directly connected to the eGPU. This avoids costly data transferts from the external GPU (making all the calculations) to the internal GPU.
In brief, everything should go one-way :
If you really want to display Millumin's interface on your MacBookPro's LCD, be sure to activate the option "Disable Workspace" (see menubar "Output"). So there will not be much data transfert via Thunderbolt/USB-C.
Lastly, you can check performances directly from Millumin, in the Monitor window (see "Window" menubar) :
To learn more about the eGPU hardware, you can read this technical post by Apple.