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There are many people in your position who accept one job in Saudi Arabia and hope they can change their visa once they get a better job offer. You can see from this thread.
Work permits for Saudi Arabia are only granted once you have a confirmed job offer. The employer acts as a sponser for you to get residence in the company and once you arrive in Saudi Arabia you have to surrender your passport to them. This also means you will be unable to leave Saudi Arabia without the comany's approval.
This basically stops people from coming into Saudi Arabia to look for work.
It is unlikely that an employer will be happy to let you go, so soon after they have supported you in getting your visa. Therefore they might make it hard for you to leave or to reapply for your visa.
For more information I would suggest having a a read of the Working in Saudi Arabia and Visas for Saudi Arabia pages.
Good luck