Very unlikely they'd let you have two passports at the same time.

I had two diplomatic passports, but was only permitted access to one at a time (while I travelled on one, the other could be in the visa mill getting prepped for my next trip.)

Most countries I would think would not let you be in posession of two valid passports at the same time.

If you have dual citizenship, that's another issue, having a passport of an other country would be fine.