TL;DR: You'll need a different laptop. More info on your requirements would be good so I can make a better reccomendation.
Right out of the gate, Microsoft says no.
Surface | External displays | Max refresh rate | Max screen resolution
Surface Book 2 15” | One | 60 Hz | 4096 x 2304
Surface Book 2 15” | Two | 30 Hz | 4096 x 2304
Surface Book 2 15” | Two | 60 Hz | 2560 x 1600
But I'm not one to believe Microsoft. After all, it is a DisplayPort 1.4 signal being carried by that USB-C connector in theory, supporting up to an 8K@60Hz signal, as confirmed by the GTX 1060 specs. 3x4K@60Hz should be no biggie, right?
Problem: How does one connect up three displays using one connector? Answer: With an MST hub! Problem: Every MST hub I know of is DisplayPort 1.2 rated, and can't support 3x4k@even 30Hz–even ones advertised for the (admittedly last gen) Surface products. (I've personally tested this one myself with a Surface Pro 4 and 2x1440p@60Hz.) Even the official Surface Dock only has two Mini DisplayPort connectors.
So while it may be possible, Microsoft certainly won't support it, and the hardware doesn't exist as far as I know.
USB-C is one of those confusing things: it refers both to a physical connector and a communications protocol. Though Thunderbolt 3 uses USB-C type connectors, they are not one and the same. The Surface Book 2 does not support Thunderbolt 3 (or any other Thunderbolt revision), and therefore cannot support eGPUs.
Without knowing your budget, use case, and the features you want, it's kinda hard to recommend a laptop. However, based off the fact that you like the Surface Book, I'll recommend the Eve V with an Akitio Node as your eGPU box. It's a direct competitor to the Surface Pro, and includes a Thunderbolt 3 port, so eGPU will work fine.
Obviously there's a lot of trade offs here: eGPUs are expensive (the Akitio Node is the cheapest reasonable box I know of and still costs $250) and take a significant performance hit, you won't get the relative safety in terms of warranty and support of an established brand like Microsoft with the Eve V (though it was reviewed well), and the Eve V isn't an outstanding performer for every workload. But–based on the information you've given me (read: give me more info)–it's the best recommendation I can make.