Could two pumps be installed in series, in constant differential pressure mode?

YES

Centrifugal pumps can be connected in series if the discharge of one pump is connected to the suction side of a second pump. Two similar pumps, in series, can operate in the same manner as a two-stage centrifugal pump. Each of the pumps is putting energy into the pumping fluid, so the resultant head is the sum of the individual heads. Some things to consider when you connect pumps in series:

Both pumps must have the same width impeller or the difference in capacities (GPM or Cubic meters/hour.) could cause a cavitation problem if the first pump cannot supply enough liquid to the second pump.

Both pumps must run at the same speed (same reason). Be sure the casing of the second pump is strong enough to resist the higher pressure.

Be sure both pumps are filled with liquid during start-up and operation. Start the second pump after the first pump is running.

YES.

THE FIRST PUMP COULD BOOST TO THE OTHER PUMP, WHICH MAY NOT BE NECESSARY TO BE IN A CONISTANT PRESSURE MODE, BUT IT CAN ACCORDING TO YOUR FURTHER REQUIREMENTS (OPTIONAL).

No if the pumps will be installed in series, they have to be in the same pressure mode.