I'm taking a couple of guesses here. Let's do a mind experiment.
Let's assume the pumps are sized correctly as a system. Let's also assume that your system curve is mostly friction (not a high static head rise). What would happen if the flow were reduced significantly.
The system resistance would decrease by the square of the system flow -- that is, the head the pump(s) would see would be reduced.
Let's say one pump is operating. What would it see? It would see the reduced system head. What would it do? It would move way out on the curve. Head would reduce to near zero (your resistance is down from the reduced to 1/9th it's value -- remember resistance goes as the square of the flow).
What happens as it goes out on the curve? You could look at your NPSH requirements, but that may not tell the story. What you would really like to see is the incipient cavitation curve. Such curves (NPSH vs. Flow) for incipient cavitation, are often "U" shaped, where the NPSH head falloff curve is flatter. The bottom of the "U" is normally around the best efficiency point.
What would the pump do, then as it's NPSH requirements suddenly got higher? It would make a lot of noise, head may fall off, and flow drop because the suction was starved.
Could this be your problem? Take a pump curve and estimate a system curve, and find out.
If you wanted to fix this problem, you would need to put flow restriction in the discharge line. This would fool the pump into thinking that the system resistance just got higher. Yes, flow would be reduced, and you'd need to turn on a second or third pump sooner, but you'd be better off.
Run a test. Scrunch down on a system discharge valve. See if the noise goes away.