I'll take a stab at this one. I think you should be able to look at the problem as three separate headloss equations.
I'm going to go through the calculation for the first pump, which pumps into the force mains from the other two pumps.
1) Determine what your flow rate needs to be.
2) Determine what your head loss would be on the line from that pump to the point where it ties to the next forcemain (based on the flow from that pump only). At this connection point, place a check valve.
3) On the next section of force main, you will need to calculate it's head loss based on the flow from pump 1 and pump 2. The pipe run for this section should consider only the distance from the tie-in to the point where it ties into the last forcemain. Another check valve would be placed here.
4) On the last section of force main, you will need to calculate head loss based on the flow from all three pumps. The pipe run for this section should consider only the distance from this tie-in point to the discharge point.
5) The total head to be overcome is then found by adding up all the headloss from any section of pipe which the pump must pump through.
For instance, the first pump must overcome the headloss from all three sections of force main. The second pump must overcome the headloss from from the last two sections of force main. The third pump must overcome the headloss from the last section of force main...keeping in mind you are calculating this headloss with all three pump flows, not just pump number three.
If this isn't clear, I can try to draw a sketch and upload it.