U2417H, four, DP MST chain, Latitude 7480

The U2417H User's Guide page 12 states,

MST Multi-Stream Transport (MST) Modes

Maximum number of external monitor that can be supported = 3

I read that as three that could be connected to the first, so four might work. You just need to test it.

Test 1 =
Latitude 7480 USB Type-C out port --> USB Type-C to DP cable --> #1 U2417H DP in port (MST On)
#1 U2417H DP out port --> U2417H DP to mDP cable --> #2 U2417H mDP in port (MST Off)

Test 2 =
Latitude 7480 USB Type-C out port --> USB Type-C to DP cable --> #1 U2417H DP in port (MST On)
#1 U2417H DP out port --> U2417H DP to mDP cable --> #2 U2417H mDP in port (MST On)
#2 U2417H DP out port --> U2417H DP to mDP cable --> #3 U2417H mDP in port (MST Off)

Test 3 =
Latitude 7480 USB Type-C out port --> USB Type-C to DP cable --> #1 U2417H DP in port (MST On)
#1 U2417H DP out port --> U2417H DP to mDP cable --> #2 U2417H mDP in port (MST On)
#2 U2417H DP out port --> U2417H DP to mDP cable --> #3 U2417H mDP in port (MST On)
#3 U2417H DP out port --> U2417H DP to mDP cable --> #4 U2417H mDP in port (MST Off)

I'm afraid you'll find laptops with integrated or hybrid/coprocessed graphics are going to max out at 3 active displays - an Intel limitation. It doesn't matter how many monitors can be physically connected - only 3 will be used. The only way around that is to use a DisplayLink USB adapter or (possibly) a PCIe eGPU Thunderbolt 3 expansion box.