Dual residency is possible. It is called "Linked Residency" and costs 2000 for one year. I have it myself, but it took a bit of a fight as my sponsor wanted me to cancel my UAE residency and claimed ignorance of this option, so it took me a few trips down to immigration myself to sort it out. Note that there is actually a sign in the immigration building that has the cost in black and white, just in case you have the same problem.