How many monitors with eGPU and MacBook Pro?

My questions relate to the Blackmagic eGPU unit.
I have a MacBook Pro 13 (2019) which supports up to two external displays in addition to the built-in display.
It has 4 Thunderbolt 3 ports I believe. I want to be able to connect 3 external displays in addition to the built-in display.
Questions:
1) If I connected a Blackmagic eGPU to my Mac via Thunderbolt, how many external displays could I connect?
2) Would the built-in display continue working if the eGPU were connected in this fashion?

This information doesn't seem to be available anywhere, either in Blackmagic's FAQ or Apple's. Might be an idea to include it.

Thanks in advance!

I think this is not a good idea, because the Mac Book Pro is going to struggle to try to feed graphics to this many devices at one time. I think a maximum of one Thunderbolt display, then using a Blackmagic monitor adapter (like a Mini Monitor) will work fine. I think going beyond this is asking for trouble.

Bear in mind that Resolve itself can only support 2 displays from the GUI. There is an option to use a third for program only, but there are issues there with color managed outputs and calibration.