Yes, this is very simple. I have had two passports for many years – they usually require a notional business reason – mine was regular travel to Iran at that time and the need to lodge a my passport for extended periods at the embassy for visa purposes – no multiple entries available at the time.
As UK passport holders we’re lucky in this regard. A Greek colleague went through hell trying to obtain a second passport and got one on condition that she always lodged the second with the Greek Embassy in London when not using it!!