1440p 144Hz is the answer. It is not out of the question. If anything, the 1070Ti was meant for very high 1440p and some 4k. If you want, go for a 4k monitor, but it won't be as good as a 1080 there.
PCPartPicker part list:
https://pcpartpicker.com/list/NmBq8K
Price breakdown by merchant: https://pcpartpicker.com/list/NmBq8K/by_merchant/
Monitor: Acer - Predator XB1 27.0" 2560x1440 165Hz Monitor ($499.99 @ Amazon)
Total: $499.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-01-08 20:35 EST-0500
1440p, 165Hz.
1080p, 240Hz. Real test for the 1070Ti if it gives 240Hz always.
PCPartPicker part list:
https://pcpartpicker.com/list/v8YF6X
Price breakdown by merchant: https://pcpartpicker.com/list/v8YF6X/by_merchant/
Monitor: ViewSonic - XG2530 25.0" 1920x1080 240Hz Monitor ($386.99 @ Amazon)
Total: $386.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-01-08 20:36 EST-0500