To sound like a expert .
I know for a fact there are only 33 countries that can get upon arrival visit visa Americans are one, it is renewal for 1extra month. Then you must leave Qatar and re enter on new visa. I have been here 10 months, there is no multiple entry visa for Qatar.
I had to leave 2 times in 6 months for a few hours to Bahrain until my family visit visa was approved for 6 months. Then work visa.