If you are workin in Saudi Arabia having a Saudi RP with a good profession is enough, as for Bahrain Visa is free (14days) if you have a saudi rp compared to other gcc were they charge you 60 dhs for a 3 day visa. Travelling to uae, kuwait and doha will be coasting 100 Dhs which is cheap enough compared to geting a separate rp. Regarding oman i dont have any idea as i have not yet visited.

You can get multiple RP in gcc, as there's no prob. One of my uncle has 3 RP thats from Saudi, Bahrain & UAE.