You folks probably commonly deal with much bigger pumps than I do.
For smaller pumps at least, I wouldn't put two pumps in series if one or both had a flat characteristic. This, in my mind, would give rise to the potential for flowrate surges and probable pulsations or oscillations in loads. This is probably more a concern in single stage pumps. In any event, if they had to be configured in series, I would try to put the downstream pump on flow control, and I would consider running the upstream pump somewhat (not too much) left of BEP if it could take it.
On shut-down sequence, I would include a timer in the control logic to shut down the downstream pump first, and a timer on start up to start the upstream pump first. This avoids the potential for the line pressure between pumps to drop to a point where you would get a big "bang" (hammer) on start-up. Of course you would need to look at all the system components to make sure that they could take the short duration pressures involved, and safeguard accordingly.
I was involved in a failure cause analysis for a system consisting of a centrifugal booster in front of a high pressure plunger pump for water injection (cavern wash). When initially put into service, on shutdown, both motors cut out but, whereas the centrifugal stopped pretty much right away, the plunger pump went through 11 full rotations before reaching full stop. There was some pressure recovery in the interconnecting piping by sucking water through the booster, but on start-up the booster had to start first. The result sounded like someone was taking a sledgehammer to the piping. It wasn't long before I was in the field looking at pieces of plungers and broken crankshafts from a disintegrated plunger pump. There were other issues at play, but the "Big Bang" certainly played a part.
Putting start-up and shutdown timers in place eliminated that part of the problem.
For the record...I was not involved in the original design.
Regards,
SNORGY.