If you mean two UK passports at the same time, it is, or used to be possible. I used to work for a big company whose staff travelled all the time, and we sometimes had to write to the Passport Office explaining that the office had to apply for a visa for a busy executive before s/he was even back from another trip. I believe that way some of their staff did indeed obtain two passports. The real reason was, of course, that they had to go to both the US and Libya, or perhaps other countries with poor diplomatic relations with each other, and they were careful to use always one passport for one country and another passport for the other country.