What is your use case for external GPU? If you need a good GPU for gaming on Linux, it is better to sell your 1080ti and get a AMD RX580 or even AMD Vega. If it is for CUDA, you can use your CPU's IGP or buy a cheap AMD GPU for desktop and only use NVIDIA for CUDA.

So unless you don't have a IGP and your motherboard doesn't have spare PCI-e slots, it is better to use a dual GPU approach of if you really need a NVIDIA card. Otherwise selling your NVIDIA card and buying a AMD one is a good choice.

Of course, YMMV and you know better than me what is good for you.