Yeah! UPSC Combined Medical Service examination has the eligibility criteria that the candidate must have passed MBBS. So after BHMS you can apply for UPSC CMS.

To know more about UPSC CMS you can visit the link below:

https://competition.careers360.com/exams/upsc-cms

There are no such examination conducted centrally like this for BHMS. But if you want to go for non-technical jobs then you can go for any exams which requires a graduation such as SSC CGL, ,IBPS PO,LIC,RBI ,UPSC,RRB. Now if you go for MD then you will have better scopes in your field in academics as well as you will get better scope and credibility for private practice also.

I hope this answer helps. All the very best for your future endeavors!