This type of arrangement, is not unusual. It is done for energy, cost or NPSH.
Examples: in some urea plants you need to provide ammonia reflux to a distillation column (low pressure) and feed the reactor (high pressure). It may be better to have a low pressure pump for the reflux and a high pressure pump for feeding the reactor. This way, you avoid the energy needed to pressurize the reflux to the reactor pressure and then wasting that energy in a control valve. You may say "OK, but you can have them in parallel", what brings us to the NPSH issue.
Multistage high pressure pumps, that normally runs at high speed (>3000/3600 RPM) have higher NPSH requirements than a single stage booster pump. So the designer is faced with a few option: more stages and lower speed on the high pressure pump, elevating all the equipment in the suction of the pump (several meters), or installing a booster with low NPSH requirements. Sometimes the later is the best option.
Another example are the pumps in reverse osmosis pre filters. If you don't have enough pressure in your water supply, you install a booster pump to feed the pre filters and then you go to the high pressure pumps. Otherwise you would have to design the filters for high pressure.
One caveat is that you need to interlock the second pump in case of loss of the first one to avoid damage, and design for the maximum pressure of the first one (suction rating, seals, etc).
Also, control strategy should prevent starving of the second pump, and may require a split range or override for the cases where you don't have enough flow in the low pressure pump to feed the required flow in the second (startup, abnormal situations, etc). And tuning the controllers to avoid interaction/cycling between controllers.
Edited by Saml, 24 May 2017 - 11:19 AM.