Assuming you are talking about a British Passport, then yes it is still possible (although the last time i did it was in 2019). In addition to the usual passport requirements you need to provide a letter from your employer explaining the reasons why you need a second passport (need to give specific examples of countries where you will be travelling that justifies the need for it, and preferably dates). There are plenty of examples of these letters if you search online.

I have done this using the 4 hour express appointment at the passport office in london and was relatively straightforward. Take copies and original of existing passports too.

Be prepared to jump through these hoops whenever you renew either passport as each renewal is considered an application for a second passport unless one of them expires or is cancelled.