Any way around letters of recommendation requirement?
Your "merits" consist of more than just your undergraduate grades. They also consist of your ability to work with others, your curiosity, your interest beyond just learning what's necessary for the test, etc. This is why we ask for letters of recommendation.

As for who exactly writes your letters, there is more leeway. I don't know about MBA programs, but in mathematics we would usually be equally happy to get letters that do not necessarily include your current supervisor. I would imagine that letters from former supervisors would be just as acceptable. The point, however, is that your supervisors can speak to your work ethic and abilities in ways nobody else can, and consequently provide important insight to the committee evaluating your application that cannot be obtained in any other way. In particular, co-workers likely have a different perspective on you than what a former supervisor sees in you.