Pulse Width Modulation to open solenoid valve in 3 stages any one know how to do this

Are you trying to slowly increase to full flow? Solenoids USUALLY have 2 positions,
Are you thinking like RC Servo?
Might be a solution using three solenoid valves.
What are you wanting to do?

Never seen you had solution. Stepper Motor?
Primitive way, Water in and split 3 ways, then these 3 conduits would have 3 solenoid valves, then through 3 1/4 Turn valves. The center valve would have no 1/4 turn valve,
Only full open, The other 2 valves would be adjusted accordingly.
Example: 1 solenoid energized, 1/2 flow, 2 solenoids energized, 3/4 flow, 3rd open, Full Flow.
Could do 1 or 2 or 3.
Or 1, 1+2, and, 1,2, and 3.