I think I've found a solution, at least for my case.
X99S XPower Gaming Titanium, according to its manual, will support a 3-Way SLI config for a 40-lane CPU of:
PCI_E1 - 3.0 x8, enough for a GTX 1070
PCI_E2 - 3.0 x8, enough for a GTX 1070
PCI_E3 - 0
PCI_E4 - 3.0 x16, enough for a 10Gb Network card
PCI_E5 - 2.0 x 1, enough for a GT 710 (it's just running a 5" terminal display)
PCI_E6 - 0
M2_1 - 3.0 x4, enough for a Samsung 950 Pro M.2 SSD
I'm just worried about airflow over the SSD, but from the looks of the chart, I think I could just swap in a U.2 drive instead.
Am I completely nuts here or could something like this actually work?