Any Dominica (Commonwealth) citizen working with Iqama here

Not a Dominican but also hold a citizenship from one of the carribean countries. 

Simple answer, forget about it.  As far as I was told, the citizenship can only be switched if they issue a work permit for that particular country.  The problem is that Saudi has no Embassy in the carribean which means that the closest Embassy to handle this case would be in the US or Canada.   To get that work permit, you are going to have to apply from there and that would be a major major hassle.  Also, these countries didn't even appear in the drop down of the MOHRE at the time I checked - back in 2018.

On top, assuming it's done and you are Pakistani and visit Pakistan (and want to keep Pakistan nationality), when you go back to Saudia from Pakistan, they will see the Dominican passport and give you crap.  It used to be relaxed some years ago but they really started cracking down on it, since last year.  A friend of mine who is based in Pakistan was travelling to Europe via Dubai and when they saw his Dominican passport, they told him to renounce Pakistan citizenship.  They told him that they entered it in the system and he won't be allowed to exit next time without renouncing it.   Even for someone like me, who was travelling to Bahrain on a Pakistan passport, they even noted down in their system, the expiry date of my Bahrain residence.  They have also implemented a question for online renewals recently i.e. "Are you a citizen of any other country". 

Lastly, for someone like me who travels between Bahrain and Saudi every week, a Pakistan passport is good as I can get a 100 page passport.............on any carribean passport, once your pages are used up, you have to renew it via mail which takes a month or so.........and you are stuck.........the Pakistan passport you can renew online prior to expiry.

So my advice is to not bother with this and complicate your life - unless you don't want Pakistan citizenship anymore.