I have four way switches on a staircase that have been wired similarly to the diagram bellow.
One switch has four wires, the other two have three.
I tried to use a combination of GE 45614 Z-Wave 3-Way On/Off Switch Kit, but did not accomplish anything useful.
Is there anyway to use z-wave switches on this?
I can easily ad neutral to each switch, in case it makes a difference.
You need the 3-way kit plus another aux switch. 3 total switches, 1 master and 2 aux. Your old switches are now paper weights. 
Each aux switch will get the red traveler wire(s) (technically just signals the master to trip), and white neutral(s), plus ground.
Master must have line (black wire from power source), load (black wire to fixture), traveler, neutral, plus ground.
You can’t wire the zwave switches like the traditional ones in the picture.
If you are lucky, the power source and the wiring to the fixture are all in the same gang box (like the last 3-way in your picture, or technically any of them).
On the master switch, just connect the power source black wire to “line”, the fixture black wire to “load”, connect both white neutral wires to “neutral”, the red wire to “traveler”, and then the bare ground wire to the green connector. The next switch will be an aux device, so connect all red wires to “traveler”, all white wires to “neutral”, use a wire nut and connect the black wires together, and then the ground to the green screw. The next aux switch will be the same as the other.
That’s a simple explanation using the picture above as reference, but if you have other wires feeding outlets or other light fixtures, you’ll need to add pigtails depending upon where and how other wires are in each gang box. It’s not super complicated, but a little more of a brain teaser.
I hoped that helped a little. I’m no electrician, but I have successfully installed 6 3-ways in my house, and 1 4-way in another home.
And don’t forget to turn off the power first
Thank you. I’ll try it and report back.
No worries. Since Lowes carries these kits, I just bought 2 so I could use the aux switch from one kit in a 4-way set up. I then used the left over master switch somewhere else in the house (just cover up the exposed traveler screw with electricians tape). You can never have enough switches…
It finaly worked. I had to get power to the same box as light fixture wire, using unused black wiresm. Thank you very much.