There are so many ways you can do this, allow me to give two suggestions if you want to use just one pump.
There is an easy way and a hard way to do this. The easy way would be to put in a throttling valve and a backpressure regulating valve downstream of the pump. The throttling valve will control your flowrate and the reg valve will maintain the pressure at a set level. You'd size your pump based upon max flow@60 psi and control the throttling valve by whatever method you choose.
The harder way is with a VFD and a throttling valve. Again, size the pump for max flow@60psi. As the flow demand drops, the VFD slows the pump (but the discharge pressure also drops). The throttling valve will close to bring the pressure up which will also cause the flowrate to drop a little more. Using a PLC to control the speed and valve position can give you ultimate control over the system to ensure that you will always have the flow you want at the pressure you need. I'd recommend a butterfly valve for the throttling valve to minimize system transients and the inevitable "hunt and search" that could follow from using an unsuitable valve (and badly set-up PLC logic) to throttle the process fluid.
Of course, the pump's shutoff head should be at least 15-20% higher than your design TDH so you won't get out of control. Also, a pump with a continually rising performance curve is a must. Lastly, you need to review the minimum flow aspects of the pump under consideration to ensure that you can get the entire range of flows that you want.
If you wanted to use more pumps then you'd minimize the amount of throttling/speed adjustments that went on and therefore might make the system a little more stable but at an obviously increased cost.
Lastly, if your system curve truly IS flat, then you don't need the throttling valves because the system curve (TDH=60 psi) will always intersect the pump curve at a TDH of 60psi no matter what the flow when you slow the pump down.
Just out of curiosity, what type of effluent process are you in that requires you to keep the discharge pressure at 60 psi?
Tim