it depends on each particular case. Person can hold both residencies in case he/she is under the same entity's sponsorship. Let's say, company "ABC" has its branches in Dubai and in Doha. your duties include frequent travelling, and you basically live in both countries. In this case you will be allowed to keep both residencies, 2 driver license, etc.
In your case it doesn't seem to be possible. But again, there are always exceptions.