You can set up multiple monitors with the GTX 1070 Ti graphics card. And you can connect 144Hz monitors. If the the two additional monitors are regular 60 Hz monitors then there isn't a problem.
The problem that can arise is that 144 Hz monitors in general require a DisplayPort or dual link DVI-D. The next problem that may arise is that 144 Hz monitors place an increased demand upon the graphics card. And as the demand on the graphics card goes up the FPS will go down. So if or instance you installed three 144 Hz monitors, then the FPS in your games may end up lower than desired. And resolutions higher than 1080P will also increase the demand on the GPU.