Am I able to change sponsors after completing one...

It should be noted that after reviewing your inquiry and legal scrutiny we would like to inform you that the sponsorship system in Qatar is no longer applied, it was canceled and the relationship became related to the contract which signed between the worker and the employer, and also related to the law regulating the entry of expatriates to Qatar
Article 21:
The employer, the Competent Authorities, and the Ministry of Labor and Social Affairs may agree to transfer the Foreign National laborer to another employer before the time limit in the contract has been reached or after five years of working for the employer if the contract did not specify a time period.
The Foreign National laborer may, with authorization from the Competent Authorities and the Ministry of Labor and Social Affairs, transfer to another employer in the event of the Recruiter’s death or dissolution of the body corporate for any reason.
In all cases, the employer serving as the Recruiter shall not have his legal rights, or the contract between him and Foreign National, violated, in accordance with the referenced Labor Law.
The aforementioned article organized the cases of which the employee can transfer to another company as follow:
• With an approval from the employer (Whatever the contract is)
• After completing five years on unfixed term contract
• The end of the fixed term contract
• The death of the employer
Therefore, you can transfer if your employer agreed then you have to submit your resignation or it may result in depriving you from entering the country once again for a year.
Therefore, if the employment contract is limited and the contract was terminated by completion of the period with the refusal of the employer to grant you Non-objection certificate, you can go to the Ministry of Labor and Social Affairs and file a complaint if you proved that the employer refused to give you the Non-objection certificate and the visa cancellation, this entity will cancel the visa and grant you permission to change work with its knowledge and permission.