Controlling header pressure with multiple Pumps

I was looking for some input to help me develop a design. We have 3 Water Injection pumps feeding a common header, where there is a Pressure transmitter. This transmitter provides the PV to 3 Pressure controllers which are controlling a Pressure Control Valve on each pump discharge. Is it possible to have the 3 pumps running and all the Pressure control valves controlling off of the Pressure transmitter downstream of the pumps at the header?

My concern is that they might fight against each other? The pumps are in parallel.