Can I hold two employement visas for Oman and Bahrain

It's a bit of a grey area.

As far as the rules are concerned (and not spelled out clearly), holding work visas for two GCC countries is a no-go. It can be possible if it's the same company in both locations and your job requires you to be working out of both locations.  The only other way to work around this is to hold one work visa and any number of investor or property based visas.

However, in reality, enforcement is patchy.  To my knowledge, only UAE and Saudi make a fuss about it sometimes.  The way around it is to get UAE/KSA first and then any other country visa.  I have myself held UAE/Bahrain and UAE/Saudi for extended periods of time and traveled in / out with no problems.

What I have heard is that in the future when they implement the one ID proposal across GCC i.e. expats being able to travel on their EIDA/CPR or resident card; this will be stopped.  But I have been hearing about this proposal for years

Out of curiosity, why would your employer keep your visa if you are resigning?